Mega quiz (updated)

Suppose your scene consists of two co-planar right triangles adjoining to make a square and two clipping planes. Also assume that you always convert any clipped results to triangles. Depending on where the clipping planes are, you could end up drawing as *few* as ___ triangles?

0 *Could clip whole thing away*

You are running the DDA algorithm, stepping in x, from (3.5, 5.0) to (8.5, 3.0). Assume that pixel centers are at integer coordinates. What is the x-coordinate of the vector you add to get from the first pixel to the second? Reply with a decimal number with at least one digit on each side of the period, like 2.3 or -5.0

1.0 *stepping in x*

In class we discussed the half-edge structure. Assuming that a vertex is made of three 4-byte values and a pointer to one half edge, and that each pointer is 4 bytes; how much memory is needed to represent the 4 triangular faces of a tetrahedron in this representation? Answer as a positive integer, like 103.

208

Suppose your scene consists of two co-planar right triangles adjoining to make a square and two clipping planes. Also assume that you always convert any clipped results to triangles. Depending on where the clipping planes are, you could end up drawing as *many* as ___ triangles?

8

Fragment composition is the process of A) combining little scenes into a larger scene B) combining per-shape pixels into a screen pixel C) running a shattering animation in reverse D) None of the above

A) combining little scenes into a larger scene *B) combining per-shape pixels into a screen pixel* C) running a shattering animation in reverse D) None of the above

A texture is a raster; the word for a single pixel in that raster is called a _________

Texel

Can't display the image on the question part. ¯\_(ツ)_/¯

even-odd

Can't display the image on the question part. ¯\_(ツ)_/¯

non-zero winding

Can't display the image on the question part. ¯\_(ツ)_/¯

something other than those two (not even-odd or non-zero winding)

Which requires the least code to write? A) BMP B) JPEG C) PNG D) SVG

*A) BMP* B) JPEG C) PNG D) SVG

The surface of a sphere modeled with several thousand small triangles Select all that apply A) Back-face culling B) Painters algorithm C) Depth buffer

*A) Back-face culling* *B) Painters algorithm* *C) Depth buffer*

When drawing a single-pixel-wide diagonal line without half-tones, A) A four-connected line will fill more pixels than an eight-connected line B) An eight-connected line will fill more pixels than a four-connected line C) Four- and eight-connected lines fill the same number of pixels D) Whether four- or and eight-connected have more filled pixels depends on line slope

*A) A four-connected line will fill more pixels than an eight-connected line* B) An eight-connected line will fill more pixels than a four-connected line C) Four- and eight-connected lines fill the same number of pixels D) Whether four- or and eight-connected have more filled pixels depends on line slope

The "golden angle" is 137.507764...°. It is used in simulating plant grow A) real plants use it B) real plants use something more complicated that it approximates C) plants don't use it, but it looks "plant-like" to many people D) plants don't use it, so it can be used to creat a feel of alien flora.

* A) real plants use it* * B) real plants use something more complicated that it approximates* C) plants don't use it, but it looks "plant-like" to many people D) plants don't use it, so it can be used to creat a feel of alien flora.

A normalized homogeneous direction or normal is a homogeneous vector where (select the most general true answer) the last coordinate is 0 the last coordinate is 1 the last coordinate is has magnitude 1 the full vector has length 1 the subvector excluding the last coordinate has length 1 none of the above; you cannot normalize directions none of the above; all homogeneous directions are normalized The following ask about coordinate space transformations

* the last coordinate is 0* the last coordinate is 1 the last coordinate is has magnitude 1 * the full vector has length 1* * the subvector excluding the last coordinate has length 1* none of the above; you cannot normalize directions none of the above; all homogeneous directions are normalized The following ask about coordinate space transformations

Which of the following expressions are true for all 3-vectors x, y, and z? Select all that apply A) (x × y) · x = 0 B) x × y = y × x C) x · y = y · x D) x × y is a number E) x × y is a vector F) x · y is a number G) x · y is a vector

*A) (x × y) · x = 0* B) x × y = y × x *C) x · y = y · x* D) x × y is a number *E) x × y is a vector* *F) x · y is a number* G) x · y is a vector

Which of the following kinds of help, if obtained, must be cited in comments in the code, according to course policy? Select all that apply A) Code you found online, tried out, but ended up not using. B) Conceptual help from a friend in the course. C) Conceptual help from a private turor. D) Code help from the professor in office hours. E) Code snippets in a Wikipedia article linked from the course website. F) Code snippets in a Wikipedia article not linked from the course schedule. G) Recordings of lecture.

*A) Code you found online, tried out, but ended up not using.* *B) Conceptual help from a friend in the course.* *C) Conceptual help from a private turor.* D) Code help from the professor in office hours. E) Code snippets in a Wikipedia article linked from the course website. *F) Code snippets in a Wikipedia article not linked from the course schedule.* G) Recordings of lecture.

Which can provide precise control over the speed at which the end of the limb approaches its goal? A) Jacobian matrix B) FABRIK C) both D) neither

*A) Jacobian matrix* B) FABRIK *C) both* D) neither

In class we discussed the half-edge structure. What is the worst-case asymptotic complexity of finding the set of adjacent vertexes of a vertex? Let F be the number of facets and V be the number of vertexes; assume that the number of sides on a facet and the number of edges sharing a vertex are O(1). A) O(1) B) O(F) C) O(V) D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2)

*A) O(1)* B) O(F) C) O(V) D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2) *Find next, find pair, find vertex* Runtime is # of neighboring vertices, and that's usually around 6

In class we discussed a simplex structure based on a pair of arrays. Consider this structure for 2-simplexes (i.e., triangles, not line segments or tetrahedrons). What is the worst-case asymptotic complexity of finding the set of adjacent vertices of a vertex? Let F be the number of facets and V be the number of vertices; assume that the number of sides on a facet is 3 and the number of edges sharing a vertex is O(1). A) O(1) B) O(F) C) O(V) D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2)

*A) O(1)* B) O(F) C) O(V) D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2) *Use neighboring simplices*

Which attempts to enumerate the set of pixels covered by an object? A) Rasterization B) Ray tracing

*A) Rasterization* B) Ray tracing

Consider the space performance of a filter as a function of s, the number of elements in the filter's largest dimension. A) Separable filters are asymptotically more space-efficient to store than non-separable filters B) Separable filters are a constant factor more space-efficient to store than non-separable filters C) Separable filters are not more space-efficient to store than non-separable filters

*A) Separable filters are asymptotically more space-efficient to store than non-separable filters* B) Separable filters are a constant factor more space-efficient to store than non-separable filters C) Separable filters are not more space-efficient to store than non-separable filters

Consider the time performance of a filter as a function of s, the number of elements in the filter's largest dimension. A) Separable filters are asymptotically more time-efficient to apply than non-separable filters B) Separable filters are a constant factor more time-efficient to apply than non-separable filters C) Separable filters are not more time-efficient to apply than non-separable filters

*A) Separable filters are asymptotically more time-efficient to apply than non-separable filters* B) Separable filters are a constant factor more time-efficient to apply than non-separable filters C) Separable filters are not more time-efficient to apply than non-separable filters

Which of the following are used for perfectly clear glass? Assume the glass is 1transparent with no other elements of appearance. Select all that apply A) Snell's law B) Lambert's law C) Total internal reflection D) External reflection

*A) Snell's law* B) Lambert's law *C) Total internal reflection* D) External reflection

If a display has gamma = 1, then A) a pixel with color (0.5, 0.5, 0.5) emits half as much light as a pixel with color (1, 1, 1) B) a pixel with color (0.5, 0.5, 0.5) emits less than half as much light as a pixel with color (1, 1, 1) C) a pixel with color (0.5, 0.5, 0.5) emits more than half as much light as a pixel with color (1, 1, 1) D) The following assume a color model with each component measured between 0 and 1. Assume H means Hue, S means Saturation, L means Lightness, and V means Value.

*A) a pixel with color (0.5, 0.5, 0.5) emits half as much light as a pixel with color (1, 1, 1)* B) a pixel with color (0.5, 0.5, 0.5) emits less than half as much light as a pixel with color (1, 1, 1) C) a pixel with color (0.5, 0.5, 0.5) emits more than half as much light as a pixel with color (1, 1, 1) D) The following assume a color model with each component measured between 0 and 1. Assume H means Hue, S means Saturation, L means Lightness, and V means Value.

Mip-mapping is used to reduce A) aliasing in distant or small textured elements B) aliasing in near or large textured elements C) blockiness in distant or small textured elements D) blockiness in near or large textured elements E) blurriness in distant or small textured elements F) blurriness in near or large textured elements

*A) aliasing in distant or small textured elements* B) aliasing in near or large textured elements C) blockiness in distant or small textured elements D) blockiness in near or large textured elements E) blurriness in distant or small textured elements F) blurriness in near or large textured elements

A translation matrix has Select all that apply A) all 1s on the main diagonal B) last column of (0, 0, 0, 1) C) last row of (0, 0, 0, 1) D) 0s everywhere except the main diagonal, last row, and last column

*A) all 1s on the main diagonal* B) last column of (0, 0, 0, 1) *C) last row of (0, 0, 0, 1)* *D) 0s everywhere except the main diagonal, last row, and last column*

De Casteljau's algorithm for finding the midpoint of a cubic Bézier curve Select all that apply A) also splits the curve in half B) works for any order Bézier curve, not just cubic curve C) only uses averaging operations (i.e., (a + b) ÷ 2) in its computation D) can also find any other point on the curve, not just the midpoint

*A) also splits the curve in half* *B) works for any order Bézier curve, not just cubic curve* *C) only uses averaging operations (i.e., (a + b) ÷ 2) in its computation* *D) can also find any other point on the curve, not just the midpoint*

Caustics A) are less efficient to generate by tracing from eye to light B) are less efficient to generate by tracing from light to eye C) can not be generated by tracing from eye to light D) can not be generated by tracing from light to eye

*A) are less efficient to generate by tracing from eye to light* B) are less efficient to generate by tracing from light to eye C) can not be generated by tracing from eye to light D) can not be generated by tracing from light to eye

Which of the following are the shallow water equations able to capture? Select all that apply A) big waves are fast waves B) waves deflect around obstacles C) the top of waves overtake the bottom, creating concavity and foam D) vorticity in water disturbs the surface behavior

*A) big waves are fast waves* *B) waves deflect around obstacles* C) the top of waves overtake the bottom, creating concavity and foam D) vorticity in water disturbs the surface behavior

Suppose your scene consists of two co-planar right triangles adjoining to make a square and two clipping planes. Also assume that you always convert any clipped results to triangles. For some fixed clipping plane and square configuration which of the following could change the number of triangles you end up with? A) changing which of the two options you use when turning quads into triangles B) changing which of the two orders you use when applying the two clipping planes

*A) changing which of the two options you use when turning quads into triangles* *B) changing which of the two orders you use when applying the two clipping planes*

Which of the following are used to create shading of matte objects? Select all that apply A) diffuse shading B) specular shading C) the Blinn-Phong reflection model D) Lambert's law E) the Phong reflection model F) the Oren-Nayar reflectance model G) the Minnaert function H) the Cook-Torrance model

*A) diffuse shading* B) specular shading C) the Blinn-Phong reflection model *D) Lambert's law* E) the Phong reflection model *F) the Oren-Nayar reflectance model* *G) the Minnaert function* H) the Cook-Torrance model

Printers use cyan, magenta, yellow, and black pigment instead of red, green, and blue, because those pigments A) each absorb a narrow band of light wavelengths B) each emit a narrow band of light wavelengths C) each reflect a narrow band of light wavelengths D) each transmit a narrow band of light wavelengths E) each absorb a broad band of light wavelengths F) each emit a broad band of light wavelengths G) each reflect a broad band of light wavelengths H) each transmit a broad band of light wavelengths

*A) each absorb a narrow band of light wavelengths* B) each emit a narrow band of light wavelengths C) each reflect a narrow band of light wavelengths D) each transmit a narrow band of light wavelengths *E) each absorb a broad band of light wavelengths* F) each emit a broad band of light wavelengths *G) each reflect a broad band of light wavelengths* *H) each transmit a broad band of light wavelengths*

Which of the following properties of fluids can not be fully resolved be considering only a limited region of the fluid? A) incompressiblity B) self-advection C) viscosity D) stuff advection

*A) incompressiblity* B) self-advection C) viscosity D) stuff advection

uniform variables are commonly used as Select all that apply A) input to a vertex shader B) input to a fragment shader C) output of a vertex shader D) output of a fragment shader E) output of the control logic (e.g., the JavaScript part of WebGL)

*A) input to a vertex shader* *B) input to a fragment shader* C) output of a vertex shader D) output of a fragment shader *E) output of the control logic (e.g., the JavaScript part of WebGL)*

attribute variables are commonly used as Select all that apply A) input to a vertex shader B) input to a fragment shader C) output of a vertex shader D) output of a fragment shader E) output of the control logic (e.g., the JavaScript part of WebGL)

*A) input to a vertex shader* B) input to a fragment shader C) output of a vertex shader D) output of a fragment shader *E) output of the control logic (e.g., the JavaScript part of WebGL)*

NURBS stands for "Non-uniform rational B-spline". "Rational" indicates A) it has an extra coordinate at each control point that the others are divided by B) it is computed using rational numbers (rather than floating-point) C) it makes more sense to artists than other curves D) the ends of the curve use the same rules as the middle E) None of the above

*A) it has an extra coordinate at each control point that the others are divided by* B) it is computed using rational numbers (rather than floating-point) C) it makes more sense to artists than other curves D) the ends of the curve use the same rules as the middle E) None of the above

Which of the following are more true of Vulkan than of OpenGL? Select all that apply A) it is new B) it is fast when run C) it is easy to use D) (accepted any answer) it is cross-platform

*A) it is new* *B) it is fast when run* C) it is easy to use D) (accepted any answer) it is cross-platform

If you transform the location of an object by M, you should transform its surface normals by the inverse transpose of M. This is because the inverse transpose of a transformation Select all that apply A) keeps rotation unchanged B) keeps scaling unchanged C) inverts rotation D) inverts scaling

*A) keeps rotation unchanged* B) keeps scaling unchanged C) inverts rotation *D) inverts scaling*

The R in BRDF indicates that it is suited for Select all that apply A) matte objects like sandpaper B) shiny objects like car paint C) clear objects like crystal balls D) phosphorescent objects like glow-in-the-dark plastics E) florescent objects like teeth under ultraviolet light F) translucent objects like paraffin wax

*A) matte objects like sandpaper* *B) shiny objects like car paint* *C) clear objects like crystal balls* D) phosphorescent objects like glow-in-the-dark plastics E) florescent objects like teeth under ultraviolet light F) translucent objects like paraffin wax

The most efficient approach to generating motion blur is to A) modify the final rendered image based on the velocity of the objects represented in each pixel B) use the velocity of the object in the lighting equation C) have multiple rays from each pixel, each shot at a slightly different time D) render at 120 fps and then average frames to get down to 30fps

*A) modify the final rendered image based on the velocity of the objects represented in each pixel* B) use the velocity of the object in the lighting equation C) have multiple rays from each pixel, each shot at a slightly different time D) render at 120 fps and then average frames to get down to 30fps

NURBS stands for "Non-uniform rational B-spline". "Non-uniform" indicates A) not all control points (or control polyline segments) have equal influence on the curve B) the ends of the curve use different rules than the middle C) there are points between curve segments were the curve is not infinitely smooth D) None of the above

*A) not all control points (or control polyline segments) have equal influence on the curve* B) the ends of the curve use different rules than the middle C) there are points between curve segments were the curve is not infinitely smooth D) None of the above

If on the first day of class I said "...which is just a linear system so we can throw it at a solver" you would A) not know what I'm talking about B) know the general idea, but be a bit fuzzy on the details C) know what I mean, but not know how to "throw it at a solver" D) know how to "throw it at a solver" in principle, but find it difficult to do E) be able to take it from there F) The following questions have nothing to do with math

*A) not know what I'm talking about* *B) know the general idea, but be a bit fuzzy on the details* *C) know what I mean, but not know how to "throw it at a solver"* *D) know how to "throw it at a solver" in principle, but find it difficult to do* *E) be able to take it from there*

The model matrix transforms between which coordinates? A) object → world B) object → camera C) world → camera D) camera → normalized device E) normalized device → device

*A) object → world* B) object → camera C) world → camera D) camera → normalized device E) normalized device → device

Phong shading interpolates Select all that apply A) pre-lit object color B) lit color C) geometric information like position, surface normal, etc

*A) pre-lit object color* B) lit color *C) geometric information like position, surface normal, etc*

Error-prone rigid body simulations are common because A) precise simulations are too expensive to compute B) precise simulations are too tedious to implement C) precise simulations can only be created for specialized cases D) precise simulations are not possible

*A) precise simulations are too expensive to compute* B) precise simulations are too tedious to implement *C) precise simulations can only be created for specialized cases* D) precise simulations are not possible

Light travels A) slower inside a material with a higher index of refraction B) slower inside a material with a lower index of refraction

*A) slower inside a material with a higher index of refraction* B) slower inside a material with a lower index of refraction

In smoothed-particle hydrodynamics, values are interpolated by A) sums of bell-curve influence fields B) linear interpolation of closest points C) nearest-neighbor interpolation from Voronoi cell membership D) solutions to a global linear system of questions

*A) sums of bell-curve influence fields* B) linear interpolation of closest points C) nearest-neighbor interpolation from Voronoi cell membership D) solutions to a global linear system of questions

Object coordinates are A) the coordinates the artist created an object B) the coordinates the artist placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

*A) the coordinates the artist created an object* B) the coordinates the artist placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

As stated in class, we can make a matrix for each bone that assists in positioning vertices around the bone. Based on what you know about matrices and transformations, such a matrix could be sufficient to capture Select all that apply A) the current position of the bone B) the current orientation of the bone C) if the bone can be stretched out, the current stretch factor of the bone D) if the bone can be bent, the current bend of the bone

*A) the current position of the bone* *B) the current orientation of the bone* *C) if the bone can be stretched out, the current stretch factor of the bone* D) if the bone can be bent, the current bend of the bone

A normalized homogeneous offset is a homogeneous vector where (select the most general true answer) A) the last coordinate is 0 B) the last coordinate is 1 C) the last coordinate is has magnitude 1 D) the full vector has length 1 E) the subvector excluding the last coordinate has length 1 F) none of the above; you cannot normalize offsets G) none of the above; all homogeneous offsets are normalized

*A) the last coordinate is 0* B) the last coordinate is 1 C) the last coordinate is has magnitude 1 D) the full vector has length 1 E) the subvector excluding the last coordinate has length 1 *F) none of the above; you cannot normalize offsets* G) none of the above; all homogeneous offsets are normalized

If a graphic paper mentions "conjugate gradient" you can safely assume Select all that apply A) they have a non-local phenomena to solve B) they have a linear system of equations to solve C) their problem is large, with many variables D) their problem is sparse, with each equation having just a few terms

*A) they have a non-local phenomena to solve* *B) they have a linear system of equations to solve* *C) their problem is large, with many variables* *D) their problem is sparse, with each equation having just a few terms*

A point represented as a homogeneous vector with three coordinates exists in A) two geometric dimensions B) three geometric dimensions C) four geometric dimensions

*A) two geometric dimensions* B) three geometric dimensions C) four geometric dimensions

Which of the following mathematical terms are you comfortable enough with that I could use them without definition? Select all that apply A) vector B) row vector vs. column vector C) homogeneous coordinates D) affine transformation E) dot product F) inner product G) 4-by-4 matrix H) matrix inverse I) gradient descent J) integral K) surface integral

*A) vector* B) row vector vs. column vector C) homogeneous coordinates D) affine transformation E) dot product F) inner product *G) 4-by-4 matrix* H) matrix inverse I) gradient descent J) integral K) surface integral

In a stress-thickening fluid, A) viscosity increases with asymmetric pressure B) viscosity decreases with asymmetric pressure C) elasticity increases with asymmetric pressure D) elasticity decreases with asymmetric pressure

*A) viscosity increases with asymmetric pressure* B) viscosity decreases with asymmetric pressure C) elasticity increases with asymmetric pressure D) elasticity decreases with asymmetric pressure

A frustum-to-box matrix has Select all that apply A) all 1s on the main diagonal B) last column of (0, 0, 0, 1) C) last row of (0, 0, 0, 1) D) 0s everywhere except the main diagonal, last row, and last column

*Select None!* A) all 1s on the main diagonal B) last column of (0, 0, 0, 1) C) last row of (0, 0, 0, 1) D) 0s everywhere except the main diagonal, last row, and last column

The diamond-square algorithm creates terrains that Select all that apply A) can have overhangs B) drain (water would not pool if pourd on them) C) are radially indepent (ridges are equally likely in any direction) D) resemble terrain weathered by hydraulic erosion E) resemble terrain weathered by thermal erosion

*Select None!* A) can have overhangs B) drain (water would not pool if pourd on them) C) are radially indepent (ridges are equally likely in any direction) D) resemble terrain weathered by hydraulic erosion E) resemble terrain weathered by thermal erosion

You are running the DDA algorithm, stepping in x, from (3.5, 5.0) to (8.5, 3.0). Assume that pixel centers are at integer coordinates. What is the y-coordinate of the vector you add to get from the first pixel to the second? Reply with a decimal number with at least one digit on each side of the period, like 2.3 or -5.0

-0.4

You are running the DDA algorithm, stepping in x, from (3.5, 5.0) to (8.5, 3.0). Assume that pixel centers are at integer coordinates. What is the x-coordinate of the vector you add to get to the first pixel? Reply with a decimal number with at least one digit on each side of the period, like 2.3 or -5.0

0.5 *Stepping in x, need to add 0.5 to go from 3.5 to next int, 4.0*

Consider the function f(x, y) = x^2 + 3 x y - y + 20. Assume we are preparing to draw the curve f(x, y) = 0 using the curve-drawing extension of DDA discussed in class. Recall that g_x is defined such that g(x + 1, y) = g(x, y) + g_x(x, y) for any g, and similarly for g_y and g(x, y + 1). *What is f_x(0, 0)? Answer as a decimal integer like "23" or "-14"*

1 a) Do f(x,y) + fx(x,y) = f(x+1,y) b) Plug in equations and solve for fx(x,y) c) Plug in #s

In class we discussed a simplex structure based on a pair of arrays. Consider this structure for 2-simplexes (i.e., triangles, not line segments or tetrahedrons). Assuming that a vertex is made of three 4-byte values and that each index and/or pointer is 4 bytes; how much memory is needed to represent the 4 triangular faces of a tetrahedron in this representation? Answer as a positive integer, like 103.

144

A cubic Bézier curve touches how many of its four control points? Answer as a number between 0 and 4, inclusive.

2

Consider the function f(x, y) = x^2 + 3 x y - y + 20. Assume we are preparing to draw the curve f(x, y) = 0 using the curve-drawing extension of DDA discussed in class. Recall that g_x is defined such that g(x + 1, y) = g(x, y) + g_x(x, y) for any g, and similarly for g_y and g(x, y + 1). *What is f(0, 0)? Answer as a decimal integer like "23" or "-14"*

20 *Just plug 0s into equation*

Consider the function f(x, y) = x^2 + 3 x y - y + 20. Assume we are preparing to draw the curve f(x, y) = 0 using the curve-drawing extension of DDA discussed in class. Recall that g_x is defined such that g(x + 1, y) = g(x, y) + g_x(x, y) for any g, and similarly for g_y and g(x, y + 1). *What is f_xy(0, 0)? Answer as a decimal integer like "23" or "-14"*

3

The following questions both ask about the second step in scan-converting a triangle: filling in the scanline between the endpoints identified in the earlier edge-scanning step. Assume that pixels are located at integer coordinates (i.e., there is a pixel at (2, 3) and not one at (2.5, 3.5)). To ensure that adjacent triangles are drawn with no gap or overlap, when filling a scanline from (7, 5) to (11, 5) how many pixels should you fill? Answer as a decimal number, like 0 or 305.

4

The following questions both ask about the second step in scan-converting a triangle: filling in the scanline between the endpoints identified in the earlier edge-scanning step. Assume that pixels are located at integer coordinates (i.e., there is a pixel at (2, 3) and not one at (2.5, 3.5)). To ensure that adjacent triangles are drawn with no gap or overlap, when filling a scanline from (7.2, 6) to (11.9, 6) how many pixels should you fill? Answer as a decimal number, like 0 or 305.

4

The following questions both ask about the second step in scan-converting a triangle: filling in the scanline between the endpoints identified in the earlier edge-scanning step. Assume that pixels are located at integer coordinates (i.e., there is a pixel at (2, 3) and not one at (2.5, 3.5)). To ensure that adjacent triangles are drawn with no gap or overlap, when filling a scanline from (7.9, 6) to (11.1, 6) how many pixels should you fill? Answer as a decimal number, like 0 or 305.

4

The signed distance between the point (2, 3, 4) and the plane 0.6x + 0.8y + 0z + 4 = 0 is ____? Answer as a decimal number, like 0.0.

7.6

HW2 and HW4 both represented polygonal objects via a list vertexes and a list of index triples. Assuming that a vertex is made of three 4-byte values and each index is 4 bytes, how much memory is needed to represent the 4 triangular faces of a tetrahedron in this representation? Answer as a positive integer, like 103.

96

Bresenham is similar to DDA, except Select all that apply A) (accepted any answer) Bresenham requires integer endpoints B) Bresenham does not require any division C) (accepted any answer) Bresenham does not require vector math D) Bresenham does not require floating-point math E) (accepted any answer) Bresenham does not generate exact line locations F) Bresenham does not suffer from round-off error

A) (accepted any answer) Bresenham requires integer endpoints *B) Bresenham does not require any division* C) (accepted any answer) Bresenham does not require vector math *D) Bresenham does not require floating-point math* E) (accepted any answer) Bresenham does not generate exact line locations *F) Bresenham does not suffer from round-off error*

Which (if any) can render "hard shadows"---that is, have arbitrarily-high-resolution crisp boundaries between shadows and lit areas? Select all that apply A) (dropped from quiz) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) (dropped from quiz) Circular shadow images B) * Flattened geometry on ground plane* C) Shadow mapping D) * Shadow volume*

Which of the following use a convolution filter? Select all that apply A) Bloom B) (accepted any answer) Tone mapping C) Parallax scrolling D) Parallax mapping E) Shadow volumes

A) * Bloom* B) (accepted any answer) Tone mapping C) Parallax scrolling D) Parallax mapping E) Shadow volumes

Which (if any) can render "soft shadows"---that is, have half-shadowed penumbras? Select all that apply A) Circular shadow images B) (accepted any answer) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) * Circular shadow images* B) (accepted any answer) Flattened geometry on ground plane C) * Shadow mapping* D) Shadow volume

Which is generally the fastest? A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) * Circular shadow images* B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

Which of the following are modeled by the golden angle (137.507764...°)? Select all that apply A) The position of seeds around a circular flower B) The angle around the trunk between on branch of a tree and the next C) The angle between a branch and its trunk D) The position of seeds around a pine cone E) The angle of one rose petal around the step compared to the next petal inward

A) * The position of seeds around a circular flower* B) * The angle around the trunk between on branch of a tree and the next* C) The angle between a branch and its trunk D) * The position of seeds around a pine cone* E) * The angle of one rose petal around the step compared to the next petal inward*

More-complicated mesh formats like a voxel grid or delaunay deformable model are needed instead of height-maps if you wish to create Select all that apply A) pocketed cliff-faces like tafoni B) water-worn shapes like fingers and gullies C) overhanging shapes like goblins, hoodoos, and arches D) laterally moving terrain like dunes

A) * pocketed cliff-faces like tafoni* B) water-worn shapes like fingers and gullies C) * overhanging shapes like goblins, hoodoos, and arches* D) laterally moving terrain like dunes

Assume you are writing code to run on a graphics card. Which of the following, if present in the code, is most likely to mean the code is not well suited to GPU-style parallelism? A) 20 copies of the same line B) for(i=0; i<20; i+=1) C) while(obj.x < 20) D) if(obj.x < 10)

A) 20 copies of the same line B) for(i=0; i<20; i+=1) *C) while(obj.x < 20)* *D) if(obj.x < 10)*

Which (if any) can cast shadows in a field of grass, where each blade shadows parts of other blades? Select all that apply A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) * Shadow volume*

Consider DDA stepping from A to B. Assume Ax is much smaller than Bx an Ay is a little smaller than By. Let D be the vector extending from A to B. The vector that moves us from one pixel to the next in a DDA line drawing algorithm is A) D B) Dx C) Dy D) length(D) E) D × Dx F) D × Dy G) D × length(D) H) D ÷ Dx I) D ÷ Dy J) D ÷ length(D)

A) D B) Dx C) Dy D) length(D) E) D × Dx F) D × Dy G) D × length(D) *H) D ÷ Dx* I) D ÷ Dy J) D ÷ length(D)

The term "per-pixel lighting" refers to A) Gouraud shading B) Phong shadng C) A technique between the above D) A technique beyond the above

A) Gouraud shading *B) Phong shadng* C) A technique between the above D) A technique beyond the above

Both Bézier curves and B-splines are curves generated from a sequence of control points. They differ in that *A)* A Bézier curve approximates (does not pass through) is control points, where a B-spline interpolates (passes through) them *B)* A B-spline approximates (does not pass through) is control points, where a Bézier curve interpolates (passes through) them *C)* A Bézier curve's control points have global influence (moving one moves the whole curve), and a B-spline's are local (moving one moves only nearby parts of the curve) *D)* A B-spline's control points have global influence (moving one moves the whole curve), and a Bézier curve's are local (moving one moves only nearby parts of the curve)a. A Bézier curve is limited in how many control points it can use, but a B-spline is not *E)* A B-spline is limited in how many control points it can use, but a Bézier curve is not *F)* None of the above

A) A Bézier curve approximates (does not pass through) is control points, where a B-spline interpolates (passes through) them B) A B-spline approximates (does not pass through) is control points, where a Bézier curve interpolates (passes through) them *C) A Bézier curve's control points have global influence (moving one moves the whole curve), and a B-spline's are local (moving one moves only nearby parts of the curve)* D) A B-spline's control points have global influence (moving one moves the whole curve), and a Bézier curve's are local (moving one moves only nearby parts of the curve)a. A Bézier curve is limited in how many control points it can use, but a B-spline is not E) A B-spline is limited in how many control points it can use, but a Bézier curve is not F) None of the above G) NURBS stands for "Non-uniform rational B-spline".

Which of the following three have the most dissimilar shape (ignoring size)? A) A pair of blobbies at the same location B) A blobbie about 1 radius distance away from another blobbie C) A blobbie about 5 radius distances away from another blobbie D) A bloobie distant from all other blobbies E) None of the above

A) A pair of blobbies at the same location *B) A blobbie about 1 radius distance away from another blobbie* C) A blobbie about 5 radius distances away from another blobbie D) A bloobie distant from all other blobbies E) None of the above

Suppose an image file contains <circle cx="20" cy="10" radius="15"/>. It is probably A) A raster image file format B) A scene description file format

A) A raster image file format *B) A scene description file format*

A separable filter is A) An n-by-1 filter B) An n-by-1 filter to be applied twice, once as its transpose C) An n-by-1 filter and a 1-by-m filter to be applied together D) A 2D filter that can be written as the product of two 1D filters E) A symmetric filter F) An antisymmetric filter

A) An n-by-1 filter B) An n-by-1 filter to be applied twice, once as its transpose C) * An n-by-1 filter and a 1-by-m filter to be applied together* D) * A 2D filter that can be written as the product of two 1D filters* E) A symmetric filter F) An antisymmetric filter

The term "water-tight", as it is used in demolition simulation, refers to A) An orientable 2D manifold B) A surface with neither edges nor self-intersections C) A structure that can build internal pressure D) A visual representation of a bounded simulation area

A) An orientable 2D manifold * B) A surface with neither edges nor self-intersections* C) A structure that can build internal pressure D) A visual representation of a bounded simulation area

Which creates the smallest file? A) BMP B) JPEG C) PNG D) SVG

A) BMP *B) JPEG* C) PNG D) SVG

Which creates the smallest file without changing any pixels? A) BMP B) JPEG C) PNG D) SVG

A) BMP B) JPEG *C) PNG* D) SVG

A rectilinear maze, rendered from the inside Select all that apply A) Back-face culling B) Painters algorithm C) Depth buffer

A) Back-face culling *B) Painters algorithm* *C) Depth buffer*

A sheet of paper folded into an S, modeled a 5 rectangles like |_|‾| Select all that apply A) Back-face culling B) Painters algorithm C) Depth buffer

A) Back-face culling *B) Painters algorithm* *C) Depth buffer*

Two cubes next to one another Select all that apply A) Back-face culling B) Painters algorithm C) Depth buffer

A) Back-face culling *B) Painters algorithm* *C) Depth buffer*

A vast carpet of multi-colored grass, where each blade is modeled as a single vertical triangle A) Back-face culling B) Painters algorithm C) Depth buffer

A) Back-face culling *B) Painters algorithm* C) Depth buffer

Two intersecting triangles Select all that apply A) Back-face culling B) Painters algorithm C) Depth buffer

A) Back-face culling B) Painters algorithm *C) Depth buffer*

Which of the following use dynamic programming? A) Blur B) Sharpen C) Edge detection D) Flood fill E) Seam carving F) Edge-following paths

A) Blur B) Sharpen C) Edge detection D) Flood fill E) * Seam carving* F) * Edge-following paths*

The Wu line drawing algorithm of a mostly-vertical line Select all that apply A) Can fill just the left part of some pixels and others completely B) Can fill just the top part of some pixels and others completely C) Can fill some pixels with brightness and others with 100% D) Is a rasterizing algorithm E) Is a ray tracing algorithm

A) Can fill just the left part of some pixels and others completely B) Can fill just the top part of some pixels and others completely *C) Can fill some pixels with 50% brightness and others with 100%* *D) Is a rasterizing algorithm* E) Is a ray tracing algorithm

Which (if any) can cast shadows on walls and chairs as well as ground? Select all that apply A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) Circular shadow images B) Flattened geometry on ground plane C) * Shadow mapping* D) * Shadow volume*

Which (if any) can have one part of a donut or inner-tube cast shadows on another part part? Select all that apply A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) Circular shadow images B) Flattened geometry on ground plane C) * Shadow mapping* D) * Shadow volume*

Which creates the fewest new polygons? A) Circular shadow images B) Flattened geometry on ground plane C) Shadow mapping D) Shadow volume

A) Circular shadow images B) Flattened geometry on ground plane C) * Shadow mapping* D) Shadow volume

In which three of the following areas of film development are software developers often engaged? Select all that apply A) Idea generation and storyboarding B) (accepted any answer) Character and setting design C) Creating rendering techniques for novel scene elements D) Character and scene modeling E) Character animation F) (accepted any answer) Fine-tuning visual effects G) Motion capture

A) Idea generation and storyboarding B) (accepted any answer) Character and setting design C) * Creating rendering techniques for novel scene elements* D) Character and scene modeling E) Character animation F) * Fine-tuning visual effects* G) * Motion capture*

We compared a raster image file to a bunch of colored dots in a grid. Putting these dots in a grid instead of scattering them at random is useful because Select all that apply A) It enables larger displays B) It makes it easy to manufacture devices to display them C) It reduces storage space needed D) It removes limits on image outline shape

A) It enables larger displays *B) It makes it easy to manufacture devices to display them* *C) It reduces storage space needed* D) It removes limits on image outline shape

Which gives sensible results when the goal is unatainable? A) Jacobian matrix B) FABRIK C) both D) neither

A) Jacobian matrix *B) FABRIK* C) both D) neither

Which is computationally more efficient? A) Jacobian matrix B) FABRIK C) they are equivalent

A) Jacobian matrix *B) FABRIK* C) they are equivalent

Which is an iterative approach, requiring multiple passes to converge on a solution? A) Jacobian matrix B) FABRIK C) both D) neither

A) Jacobian matrix B) FABRIK *C) both* D) neither

Which is based on a linear approximation of the fundamentally nonlinear behavior of rotating joints? A) Jacobian matrix B) FABRIK C) both D) neither

A) Jacobian matrix B) FABRIK *C) both* D) neither

Which works for rigs with many joints on a single limb? A) Jacobian matrix B) FABRIK C) both D) neither

A) Jacobian matrix B) FABRIK *C) both* D) neither

HW2 and HW4 both represented polygonal objects via a list vertexes and a list of index triples. What is the worst-case asymptotic complexity of finding the set of adjacent vertexes of a vertex? Let F be the number of facets and V be the number of vertexes; assume that the number of sides on a facet and the number of edges sharing a vertex are O(1). A) O(1) B) O(F) C) O(V) D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2)

A) O(1) *B) O(F)* *C) O(V)* D) O(F V) E) O(F2) F) O(V2) G) O(F2 V) H) O(F V2) *For each face, if that face includes the vertex, then the other 2 vertexes in the face are adjacent*

By using a fixed grid, detecting the collisions n of spheres all of the same radius can be made to be which of the following? Assume that most spheres do not intersect. A) O(1) B) O(log(n)) C) O(n) D) O(n log(n)) E) O(n^2^) F) O(n^3^)

A) O(1) B) O(log(n)) *C) O(n)* D) O(n log(n)) E) O(n^2^) F) O(n^3^)

Which of the following best describes the asymptotic time complexity of single-treaded, non-optimized, drawing algorithms? Let S = screen width = screen height (in pixels) O = number of objects in scene T = number of triangles in the average object P = number of pixels covered by average triangle in the scene What are the terms for raytracing? Select all that apply A) S B) S2 C) O D) O2 E) T F) T2 G) P H) P2

A) S *B) S2* *C) O* D) O2 *E) T* F) T2 G) P H) P2

Which of the following best describes the asymptotic time complexity of single-treaded, non-optimized, drawing algorithms? Let S = screen width = screen height (in pixels) O = number of objects in scene T = number of triangles in the average object P = number of pixels covered by average triangle in the scene What are the terms for rasterizing? Select all that apply A) S B) S2 C) O D) O2 E) T F) T2 G) P H) P2

A) S B) S2 *C) O* D) O2 *E) T* F) T2 *G) P* H) P2

In class we said that a spatial bounding hierarchy (also known as a bounding volume hierarchy) made some part of ray tracing logarithmic instead of polynomial, but didn't say what. Given how these hierarchies work, which term(s) get(s) a log applied? Select all that apply A) S^2 = pixels on the screen B) T = triangles in the scene C) AA = number of anti-aliasing passes per pixel

A) S^2 = pixels on the screen *B) T = triangles in the scene* C) AA = number of anti-aliasing passes per pixel

Which of the following are used for matte surfaces? Assume the surface is 1diffuse with no shine or transparency. Select all that apply A) Snell's law B) Lambert's law C) Total internal reflection D) External reflection

A) Snell's law *B) Lambert's law* C) Total internal reflection D) External reflection

Which of the following are used for perfect mirrors? Assume the glass is 1reflective with no other elements of appearance. Select all that apply A) Snell's law B) Lambert's law C) Total internal reflection D) External reflection

A) Snell's law B) Lambert's law C) Total internal reflection *D) External reflection*

Subdivision fractals are used to generate terrain because A) Some terrains are fractal B) Terrain is not fractal, but some fractals embody a few "terrain-like" characteristics. C) Terrain is not fractal, so fractal terrain can create a feel of an alien environment D) Terrain resembles fractals when viewed from the right distance

A) Some terrains are fractal * B) Terrain is not fractal, but some fractals embody a few "terrain-like" characteristics.* C) Terrain is not fractal, so fractal terrain can create a feel of an alien environment * D) Terrain resembles fractals when viewed from the right distance*

L-system fractals are used to generate trees because A) Some trees are fractal B) Trees are not fractal, but some fractals embody a few "tree-like" characteristics. C) Trees are not fractal, so fractal trees can create a feel of an alien environment D) Trees resemble fractals when viewed from the right distance

A) Some trees are fractal * B) Trees are not fractal, but some fractals embody a few "tree-like" characteristics.* C) Trees are not fractal, so fractal trees can create a feel of an alien environment * D) Trees resemble fractals when viewed from the right distance*

Most humans have four kinds of photoreceptors in their retna, but only three are active are a time; this is because A) The cones are overloaded with too much light B) The cones are starved with not enough light C) The rods are overloaded with too much light D) The rods are starved with not enough light

A) The cones are overloaded with too much light B) The cones are starved with not enough light *C) The rods are overloaded with too much light* D) The rods are starved with not enough light

Which of the following properties is true of trees in moist areas but not deserts? A) They are green B) They position their branches to maximize light expsure C) The total cross-sectional area after branching is approximately equal to the cross-sectional area before branching D) They use the golden angle

A) They are green B) They position their branches to maximize light expsure C) * The total cross-sectional area after branching is approximately equal to the cross-sectional area before branching* D) They use the golden angle

Many graphics libraries have a quaternion-to-matrix conversation function. Based on what quaternions are used to represent, the resulting matrix could be Select all that apply A) a (non-zero) translation B) a (non-identity) rotation C) a (non-one) scaling D) a (non-identity) reflection

A) a (non-zero) translation *B) a (non-identity) rotation* C) a (non-one) scaling D) a (non-identity) reflection

Which of the following require a change in surface mesh topology to simulate? Select all that apply A) a cube becomes a sphere B) a sphere becomes a donut C) a donut becomes a tube D) a tube becomes a cube E) a cube breaks into two cubes F) two cubes merge into one cube G) two hemispherical bowls become a hollow sphere H) two solid hemispheres become a solid sphere

A) a cube becomes a sphere * B) a sphere becomes a donut* C) a donut becomes a tube * D) a tube becomes a cube* * E) a cube breaks into two cubes* * F) two cubes merge into one cube* * G) two hemispherical bowls become a hollow sphere* * H) two solid hemispheres become a solid sphere*

The exact time of collision of two spheres moving with no external forces can be found via A) a linear equation (of one variable) B) a quadratic equation (of one variable) C) the solution of a linear system of equations D) a convex optimization problem E) a non-convex optimization problem

A) a linear equation (of one variable) *B) a quadratic equation (of one variable)* C) the solution of a linear system of equations D) a convex optimization problem E) a non-convex optimization problem

Multiplying a vector by a positive number (e.g., 3x) results in A) a number B) a vector pointing in the same direction as the original vector C) a vector with the same magnitude (or length) as the original vector D) none of the above

A) a number *B) a vector pointing in the same direction as the original vector* C) a vector with the same magnitude (or length) as the original vector D) none of the above

The vector between points p1 and p2 can be found by A) adding one point to the other B) dividing one point by the other C) multiplying one point by the other D) subtracting one point from the other E) none of the above

A) adding one point to the other B) dividing one point by the other C) multiplying one point by the other *D) subtracting one point from the other* E) none of the above

A rotation matrix has Select all that apply A) all 1s on the main diagonal B) last column of (0, 0, 0, 1) C) last row of (0, 0, 0, 1) D) 0s everywhere except the main diagonal, last row, and last column

A) all 1s on the main diagonal *B) last column of (0, 0, 0, 1)* *C) last row of (0, 0, 0, 1)* D) 0s everywhere except the main diagonal, last row, and last column

Depth of field is created by generating multiple rays for a single pixel, where A) all rays share the same origin but have slightly different directions B) all rays share the same direction but have slightly different origins C) each ray has a unique origin and direction

A) all rays share the same origin but have slightly different directions B) all rays share the same direction but have slightly different origins *C) each ray has a unique origin and direction*

Suppose you have a model of a right-side-up chair centered at the origin, and you want to draw an up-side-down chair centered at (10, 0, 0). Let R be a rotation matrix that flips the chair over and T be a translation matrix that adds 10 to x. Which of the following describes how to get that transformed chair? A) chair R T B) chair T R C) R T chair D) T R chair

A) chair R T B) chair T R C) R T chair *D) T R chair* *Rotate before you translate*

If we fix S=0 Select all that apply A) color changes with H but not L B) color changes with L but not H C) color does not depend on H or L D) color changes with both H and L E) the answer is different for the HSL and HSV models

A) color changes with H but not L *B) color changes with L but not H* C) color does not depend on H or L D) color changes with both H and L E) the answer is different for the HSL and HSV models

If we fix L=0 Select all that apply A) color changes with H but not S B) color changes with S but not H C) color does not depend on H or S D) color changes with both H and S

A) color changes with H but not S B) color changes with S but not H *C) color does not depend on H or S* D) color changes with both H and S *All black*

If we fix L=1 Select all that apply A) color changes with H but not S B) color changes with S but not H C) color does not depend on H or S D) color changes with both H and S

A) color changes with H but not S B) color changes with S but not H *C) color does not depend on H or S* D) color changes with both H and S *All white*

If we fix V=0 Select all that apply A) color changes with H but not S B) color changes with S but not H C) color does not depend on H or S D) color changes with both H and S

A) color changes with H but not S B) color changes with S but not H *C) color does not depend on H or S* D) color changes with both H and S *always black*

If we fix V=1 Select all that apply A) color changes with H but not S B) color changes with S but not H C) color does not depend on H or S D) color changes with both H and S

A) color changes with H but not S B) color changes with S but not H C) color does not depend on H or S *D) color changes with both H and S*

A co-dimensional fluid simulation is one that A) combines separate rules for the x, y, and z dimensions of the fluid B) simultaneously treats a single region of the fluid as both a surface and a volume C) treats some regions of the fluid as a surface, others as a volume D) solves the stress-response, incompressibility, and elasticity of a fluid together E) Regarding the shallow water equations,

A) combines separate rules for the x, y, and z dimensions of the fluid B) simultaneously treats a single region of the fluid as both a surface and a volume *C) treats some regions of the fluid as a surface, others as a volume* D) solves the stress-response, incompressibility, and elasticity of a fluid together E) Regarding the shallow water equations,

High-end non-real-time graphics simulations of fracturing and shattering A) compute strain, and use that to determine where the material breaks B) compute stress, and use that to determine where the material breaks C) model solids as discrete chunks that can come apart D) model solids as fluids with very high viscosity E) use fractals to simulate how cracks propagate F) use Voronoi diagrams to simulate how cracks propagate

A) compute strain, and use that to determine where the material breaks *B) compute stress, and use that to determine where the material breaks* C) model solids as discrete chunks that can come apart D) model solids as fluids with very high viscosity E) use fractals to simulate how cracks propagate F) use Voronoi diagrams to simulate how cracks propagate

Regarding the shallow water equations, It simplifies general fluid simulation by A) considering only horizontal motion along the surface B) considering only vertical motion of the surface C) considering only the behavior of large waves moving quickly D) considering only the behavior of surface details on a flat model

A) considering only horizontal motion along the surface *B) considering only vertical motion of the surface* C) considering only the behavior of large waves moving quickly D) considering only the behavior of surface details on a flat model

The method of separating axes is used to A) detect concave intersections B) detect convex intersections C) detect both concave and convex intersections D) resolve elastic collisions E) resolve inelastic collisions F) resolve both elastic and inelastic collisions

A) detect concave intersections *B) detect convex intersections* *C) detect both concave and convex intersections* D) resolve elastic collisions E) resolve inelastic collisions F) resolve both elastic and inelastic collisions

Which of the following are used to create shine spots? Select all that apply A) diffuse shading B) specular shading C) the Blinn-Phong reflection model D) Lambert's law E) the Phong reflection model F) the Oren-Nayar reflectance model G) the Minnaert function H) the Cook-Torrance model

A) diffuse shading *B) specular shading* *C) the Blinn-Phong reflection model* D) Lambert's law *E) the Phong reflection model* F) the Oren-Nayar reflectance model G) the Minnaert function *H) the Cook-Torrance model*

Computer screens use red, green, and blue light because those colors are A) enough to produce all other visible colors B) enough to produce most other visible colors, and adding more is not cost effective C) enough to produce a minority of visible colors, but people are not good at recognizing the others D) not ideal, but they are easier to produce

A) enough to produce all other visible colors *B) enough to produce most other visible colors, and adding more is not cost effective* C) enough to produce a minority of visible colors, but people are not good at recognizing the others D) not ideal, but they are easier to produce

Elastoviscosity is simulated by a combination of viscosity and A) fixed spring forces between fluid particles B) time-varying spring forces between fluid particles C) fixed forces on boundary fluid particles D) time-varying forces on boundary fluid particles

A) fixed spring forces between fluid particles *B) time-varying spring forces between fluid particles* C) fixed forces on boundary fluid particles D) time-varying forces on boundary fluid particles

An affine transformation can include Select all that apply A) frustum perspective B) mirroring C) scaling D) rotations E) translations

A) frustum perspective *B) mirroring* *C) scaling* *D) rotations* *E) translations*

A linear transformation can include Select all that apply A) frustum perspective B) mirroring C) scaling D) rotations E) translations

A) frustum perspective *B) mirroring* *C) scaling* *D) rotations* E) translations

A shadow ray A) goes from a point in the scene toward the eye B) goes from a point in the scene toward the light C) goes from the eye toward a point in the scene D) goes from the light toward a point in the scene

A) goes from a point in the scene toward the eye *B) goes from a point in the scene toward the light* C) goes from the eye toward a point in the scene *D) goes from the light toward a point in the scene*

Barycentric coordinates for a triangle tell us Select all that apply A) how large the triangle is B) if a point is in the triangle C) where a point is in the triangle D) which vertex of a triangle a point is closest too E) where the triangle is in the scene F) how to interpolate vertex attributes to a point

A) how large the triangle is *B) if a point is in the triangle* *C) where a point is in the triangle* *D) which vertex of a triangle a point is closest too* E) where the triangle is in the scene *F) how to interpolate vertex attributes to a point*

Dipoles with one positive and one negative light are used to render subsurface scattering. Dipoles were derived for infinite flat slabs of uniform scattering material; for that case, the visual effect of dipole lighting is A) identical to actual subsurface scattering B) identical to actual subsurface scattering, except it is missing single-scattering C) an approximation of actual subsurface scattering D) an approximation of actual subsurface scattering, except it is missing single-scattering E) an approximation that looks "subsurface-scatter-like" but does not approximate any actual material

A) identical to actual subsurface scattering B) identical to actual subsurface scattering, except it is missing single-scattering * C) an approximation of actual subsurface scattering* * D) an approximation of actual subsurface scattering, except it is missing single-scattering* E) an approximation that looks "subsurface-scatter-like" but does not approximate any actual material

Consider DDA stepping from A to B. Assume Ax is much smaller than Bx an Ay is a little smaller than By. Let D be the vector extending from A to B. If A and B are two vertices of a triangle we are filling, DDA should step between A and B A) in x B) in y C) neither one D) it doesn't matter

A) in x *B) in y* C) neither one D) it doesn't matter *Always step in y*

varying variables are commonly used as Select all that apply A) input to a vertex shader B) input to a fragment shader C) output of a vertex shader D) output of a fragment shader E) output of the control logic (e.g., the JavaScript part of WebGL)

A) input to a vertex shader *B) input to a fragment shader* *C) output of a vertex shader* D) output of a fragment shader E) output of the control logic (e.g., the JavaScript part of WebGL)

If a piece of real-time graphics code is called a "shader", you can infer that (pick the most specific correct answer) A) it computes colors B) it computes the shade of a single color C) it interpolates across triangles D) it runs on the graphics card E) it works on fragments F) it works on vertices

A) it computes colors B) it computes the shade of a single color C) it interpolates across triangles *D) it runs on the graphics card* E) it works on fragments F) it works on vertices

If a ray-tracer wants to simulate 30fps camera-style motion blur, it should A) modify the final rendered image based on the velocity of the objects represented in each pixel B) use the velocity of the object in the lighting equation C) have multiple rays from each pixel, each shot at a slightly different time D) render at 120 fps and then average frames to get down to 30fps

A) modify the final rendered image based on the velocity of the objects represented in each pixel B) use the velocity of the object in the lighting equation *C) have multiple rays from each pixel, each shot at a slightly different time* D) render at 120 fps and then average frames to get down to 30fps

The B in BRDF indicates that the RDF is the same A) no matter how the object is oriented relative to the light B) no matter how the eye is oriented relative to the light C) no matter how the object is oriented relative to the eye D) if you swap the position of the object and the eye E) if you swap the position of the eye and the light F) if you swap the position of the object and the light

A) no matter how the object is oriented relative to the light B) no matter how the eye is oriented relative to the light C) no matter how the object is oriented relative to the eye D) if you swap the position of the object and the eye *E) if you swap the position of the eye and the light* F) if you swap the position of the object and the light

The major source of numerical damping we discussed is caused by A) numerical error in incompressiblity solving B) numerical error in self-advection solving C) fixed-grid requiring averaging in incompressiblity solving D) fixed-grid requiring averaging in self-advection solving

A) numerical error in incompressiblity solving B) numerical error in self-advection solving C) fixed-grid requiring averaging in incompressiblity solving *D) fixed-grid requiring averaging in self-advection solving*

The modelview matrix transforms between which coordinates? A) object → world B) object → camera C) world → camera D) camera → normalized device E) normalized device → device

A) object → world *B) object → camera* C) world → camera D) camera → normalized device E) normalized device → device

The view matrix transforms between which coordinates? A) object → world B) object → camera C) world → camera D) camera → normalized device E) normalized device → device

A) object → world B) object → camera *C) world → camera* D) camera → normalized device E) normalized device → device

The projection matrix transforms between which coordinates? A) object → world B) object → camera C) world → camera D) camera → normalized device E) normalized device → device

A) object → world B) object → camera C) world → camera *D) camera → normalized device* E) normalized device → device

The coordinate transformation that is generally not done with a matrix is A) object → world B) object → camera C) world → camera D) camera → normalized device E) normalized device → device F) The following ask about coordinate space names

A) object → world B) object → camera C) world → camera D) camera → normalized device *E) normalized device → device* F) The following ask about coordinate space names

Consider a mass-spring model of a rope with 3 masses each connected to only their immediate neighbors. Using local-only spring resolution, if one endpoint is moved a long distance and held there, how long will it take for the other endpoint to move the same distance? Assume there is no gravity or other outside force being applied. A) one time step B) about 3 time steps C) between 1 and 3 time steps, depending on the simulation order D) a finite number greater than 3 time steps E) it depends on the spring constants F) it will never move that far

A) one time step B) about 3 time steps C) between 1 and 3 time steps, depending on the simulation order D) a finite number greater than 3 time steps *E) it depends on the spring constants* F) it will never move that far

You see an equation in homogeneous coordinates that adds normalized homogeneous vectors p and q. You can infer that A) p and q both have a w coordinate of 0 B) p and q both have a w coordinate of 1 C) either p has a w coordinate of 1 and q has a w coordinate of 0, or the opposite D) either p or q has a w coordinate of 0, or both E) either p or q has a w coordinate of 1, or both

A) p and q both have a w coordinate of 0 B) p and q both have a w coordinate of 1 C) either p has a w coordinate of 1 and q has a w coordinate of 0, or the opposite *D) either p or q has a w coordinate of 0, or both* E) either p or q has a w coordinate of 1, or both

Gouraud shading interpolates Select all that apply A) pre-lit object color B) lit color C) geometric information like position, surface normal, etc

A) pre-lit object color *B) lit color* C) geometric information like position, surface normal, etc

Which of the following components of HW2's rasterizer are fixed functionality (i.e., not arbitrarily programmable) on current graphics cards? A) specifying vertex data (positions, normals, colors, etc) B) applying the model/view and projection matrices C) dividing by w D) applying the depth buffer E) screen clipping F) computing useful matrices (rotate, scale, frustum, etc)

A) specifying vertex data (positions, normals, colors, etc) B) applying the model/view and projection matrices C) dividing by w *D) applying the depth buffer* *E) screen clipping* F) computing useful matrices (rotate, scale, frustum, etc)

In staggered grid Lagrangian fluid dynamics, values are interpolated by A) sums of bell-curve influence fields B) linear interpolation of closest points C) nearest-neighbor interpolation from Voronoi cell membership D) solutions to a global linear system of questions

A) sums of bell-curve influence fields *B) linear interpolation of closest points* C) nearest-neighbor interpolation from Voronoi cell membership D) solutions to a global linear system of questions

View coordinates are A) the coordinates the artist created an object B) the coordinates the artist created placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

A) the coordinates the artist created an object B) the coordinates the artist created placed an object *C) the coordinates defined by camera location and orientation* D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

Normalized device coordinates are A) the coordinates the artist created an object B) the coordinates the artist created placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

A) the coordinates the artist created an object B) the coordinates the artist created placed an object C) the coordinates defined by camera location and orientation *D) the coordinates where everything to be drawn is in a unit box* E) the coordinates where +1 in x means 1 pixel to the right

Device coordinates are A) the coordinates the artist created an object B) the coordinates the artist created placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

A) the coordinates the artist created an object B) the coordinates the artist created placed an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box *E) the coordinates where +1 in x means 1 pixel to the right*

World coordinates are A) the coordinates the artist used to create an object B) the coordinates the artist used to position an object C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

A) the coordinates the artist used to create an object *B) the coordinates the artist used to position an object* C) the coordinates defined by camera location and orientation D) the coordinates where everything to be drawn is in a unit box E) the coordinates where +1 in x means 1 pixel to the right

A normalized homogeneous point is a homogeneous vector where (select the most general true answer) A) the last coordinate is 0 B) the last coordinate is 1 C) the last coordinate is has magnitude 1 D) the full vector has length 1 E) the subvector excluding the last coordinate has length 1 F) none of the above; you cannot normalize points G) none of the above; all homogeneous points are normalized

A) the last coordinate is 0 *B) the last coordinate is 1* *C) the last coordinate is has magnitude 1* D) the full vector has length 1 E) the subvector excluding the last coordinate has length 1 F) none of the above; you cannot normalize points G) none of the above; all homogeneous points are normalized