FINAL 3421
What is the new point after the xyz point (3, 2, 1) is scaled by (4, 5, 6) where 4 scales x, 5 scales y, and 6 scales z?
(12,10,6)
What is the normal vector to a plane with the following equation: 3x - 5y + 4z = 1?
(3, -5, 4)
In eye space, the camera is located at the origin and pointing in what direction?
-n axis
To determine whether or not a point is inside or outside a polygon in a 2-dimensional plane, how many ray-edge intersections indicate that a point is outside the polygon in all cases if the ray only intersects edges?
0 or even number of intersections
You define a line parametrically with two points (the end points). Which parametric value(s) define the end points of the line? Select exactly TWO answers.
0,1
which scalar value is a multiplicative identity
1
Let vector v = (1, 2, 3) and vector w = (3, 2, 1). What is v • w, where • is the dot product?
10
initial dimensions of plane gameobject
10mx10m
What is the degree of a Lagrange polynomial when given three control points?
2
How many lerps are needed to compute bilinear interpolation (as described in lecture)?
3
What is the degree of a Bezier curve when given four control points?
3
What is the degree of the blending function L1(x) when using a Lagrange polynomial with four control points?
3
Order the spaces of the graphics pipeline according to which space is encountered first. Choose 1 for the first space encountered in the graphics pipeline, choose 2 for the second space, etc. Eye Space: 3 Screen Space: 5 World Space: 2 Image Space: 4 Object Space: 1
35241
Let a = sqrt(2)/2. What rotation angle does the complex number a + ai represent, where i =sqrt( −1) ?
45 deg
How many multiplications are needed to evaluate a 5th degree polynomial using Horner's method, aka Horner's rule?
5
How many lerp operations are needed to evaluate a Cubic Bezier curve using the De Casteljau algorithm?
6
Which type of continuity describes a discontinuous function (curve)? a) C-1 b) C0 c) C1 d) C2
A
What is the difference between a point and a vector? Why is this important?
A point represents a specific location in space, while a vector represents a direction and magnitude. Understanding this difference is crucial in graphics and physics simulations as it affects how transformations are applied and how objects' positions and movements are calculated.
Which boid rule averages the headings of all neighboring boids in its field of view?
ALIGNMENT
What is true for every convex polygon?
All interior angles are less than 180 degrees
Which boid rule steers a boid towards the average position of neighboring boids in its field of view?
COHESION
A line that connects two different points inside a polygon is not entirely contained within the polygon. What type of polygon is this?
CONCAVE
Which two-dimensional bounding volume would be the most appropriate for an object with a hexagonal shape?
CONVEX HULL
What winding order does Unity use to identify the front face of a polygon?
Clockwise
6. List the various types of light sources covered in class
Common light sources in graphics include: Point lights Directional lights Spotlights Ambient lights Area lights
Which illumination type(s) involves the use of the cosine function? Select all that apply.
DIFFUSE,SPECULAR
Which type of light source has parallel light rays?
Directional
Which type of collision results in motion after the collision?
ELASTIC
What is TRUE about a Finite State Machine (FSM)
Encodes all possible behaviors for a game character
Is the following statement TRUE or FALSE? "A reflex agent may be equipped with Goal Oriented Action Planning (GOAP)"
FALSE
Which control point(s) will a cubic Bezier curve interpolate?
FIRST AND LAST CONTROL POINTS
Hooke's Law models the behavior of a spring in a vacuum with the equation -ks(Lcurrent - Lrest). What kind of value is evaluated from this equation?
FORCE
What term describes the phenomenon caused by perspective projection where objects further away project onto a smaller footprint on the screen?
FORESHORTENING
Which shading approach applies a single color to each polygon?
Flat
Which illumination type allows for shadows?
Global
What is NOT an explicitly defined input parameter to define the eye space coordinate frame, i.e. the u-v-n coordinate axis?
LOOK AT VECTOR
What is not an explicitly defined input parameter to define the eye space coordinate frame, i.e. the u-v-n coordinate axis?
LOOK AT VECTOR
What is NOT an attribute of specular reflection?
Light is reflected equally in all directions
Which is NOT an attribute of diffuse illumination (reflection)?
Light is reflected in only some directions (i.e., NOT all directions)
Two AABB's, box1 and box2, are defined in the x-y cartesian coordinate space. You project the boxes along each axis as shown below: | | | | | | | ___________ _______________
NO
You want to compute the collision response of a moving point bouncing (reflecting) off an axially aligned wall or floor in a 2D space. What will you do to the point's coordinates to compute its reflection after the collision?
Negate one of the coordinates
In a perspective projection, what is the location of the center of projection?
ORIGIN
3. What is the difference between a point and a vector? Why is this important?
Orthonormal basis vectors are a set of vectors that are all orthogonal (perpendicular) to each other and have unit length (norm of 1). They are desirable because they simplify many mathematical operations in linear algebra, particularly in 3D graphics, by providing a simple and stable way to represent directions and rotations.
Describe orthonormal basis vectors. When and why are they are desirable?
Orthonormal basis vectors are a set of vectors that are all orthogonal (perpendicular) to each other and have unit length (norm of 1). They are desirable because they simplify many mathematical operations in linear algebra, particularly in 3D graphics, by providing a simple and stable way to represent directions and rotations.
When a new term is added to Hooke's Law, i.e. -ks(Lcurrent - Lrest) - kdVspring, what is the behavior of the spring after it is compressed?
Oscillates for a while and then stops
Hooke's Law models the behavior of a spring in a vacuum with the equation -ks(Lcurrent - Lrest). What will be the behavior of the spring after it is compressed?
Oscillates forever
You define a Cubic Bezier curve with the control points P0, P1, P2, and P3. How do you calculate the tangent vector to the curve at P0?
P1-P0
What term refers to the collection of values that are read from all sensors of an AI agent?
PERCEPT
Which shading approach has the best chance to reliably capture hot spots on an object's surface?
PHONG
The figure above illustrates an obstacle enclosed within a bounding circle and a boid with position P and heading V. The location B can be calculate with the equation: B = P + (|C - P| - t)U + sW. What type of value is sum of the first two terms P + (|C - P| - t)U ? [PIC]
POINT
Which component of a Learning-based agent has the agent try an action it has not taken before?
PROBLEM GENERATOR
What term refers to the portion of a reflectance model that describes light leaving a surface?
RADIOSITY
Which agent type best describes the behavior of a boid?
REFLEX AGENT
Which boid rule steers a boid away via position from neighboring boids in its field of view to avoid crowding?
SEPARATION
Which illumination type models hot spots on object surfaces?
SPECULAR
A 2D object has four vertices in the x-y cartesian coordinate space:: (-1, 1), (1, 1), (1, -1), (-1, -1). You want to compute a tight bounding circle that encloses the object. What is the radius of the bounding circle? Note: sqrt below means square root below.
SQRT2
The specular illumination calculation includes an exponent, which is called a "shininess" parameter (called n in the lecture notes). What characteristic of a hot spot does this exponent determine?
Size of the specular highlight (hot spot)
In Unity, what applies a transformation relative to the local coordinate system?
Space.Self
which class includes a property called position
TRANSFORM
Detail the steps taken in a render loop using a Unity script. E.g., methods called, etc
The Unity rendering loop typically involves the following methods:Update: Called once per frame. Used for most game logic.LateUpdate: Called after all Update methods. Useful for camera movement.FixedUpdate: Called every physics step. Used for physics-based updates.OnPreRender, OnRenderObject, OnPostRender: Used for custom rendering actions before and after the main rendering.OnGUI: For rendering and handling GUI events. Unity handles the rendering of each camera and other internal processes between these calls.
4. Show the three-dimensional rotation matrix that rotates θ degrees about the y-axis
The rotation matrix for rotating θ degrees about the y-axis is: (cos(�)0sin(�)010−sin(�)0cos(�))⎝⎛cos(θ)0−sin(θ)010sin(θ)0cos(θ)⎠⎞
A polygon is part of a polygonal mesh defining the surface of a 3D object. What direction will the face normal of the polygon point towards?
Towards points outside the 3D object
What is the formula to normalize a vector called v?
V/|V|
Which degree of freedom would allow a boid in 3D space to turn left or right?
YAW
In a perspective projection, will the projection of two lines that are parallel to the y-axis be parallel?
YES
Two circles are defined in the x-y cartesian coordinate space: Circle C1 has its center at the origin with radius 1 Circle C2 has its center at (1.25, 0) with radius 0.5 Is there a collision between circles C1 and C2?
YES
Let vector v = (3, 2, 1) and vector w = (1, 2, 3). Using the dot product, what is the angle between the two vectors?
acute
When using parenting in a scene graph, if a translation is applied to a tree node n, which other tree node(s) does it also apply, if any?
all decendants of tree node n
Which illumination model is an approximation to global illumination?
ambient
What statement below best describes how to define a rotation using Euler angles?
any order - all above
Which curve continuity characterizes a curve that is continuous on the 1st derivative but not the 2nd derivative? a) C-1 b) C0 c) C1 d) C2
c
What defines the direction that the camera points?
center of interest
A quaternion q is expressed using the following notation [w v], where v is a vector. If quaternion q represents a 60 degree rotation, what is w?
cos(30)
Which method of defining an orientation can lead to Gimbal Lock?
euler angles
When modelling a string with a sequence of springs, what are the forces that may act upon the system?
external,internal,structural
Let A be a matrix with dimensions n x k. Let B be a matrix with dimensions k x m. Is this statement true or false? AB = BA
false
What condition does Euler angles suffer from?
gimbal lock
5. Write the lighting equation developed by Phong
he Phong lighting model is given by: I=Ia+Id⋅(N⋅L)+Is⋅(R⋅V)n Where �I is the total illumination, ��Ia is ambient light, ��Id is diffuse reflection, ��Is is specular reflection, �N is the normal vector, �L is the light direction, �R is the reflection direction, �V is the view direction, and �n is the shininess coefficient.
An affine transformation has the following form: [xy1] What is the third coordinate called?
homogenous coordinates
The kinetic energy of a moving object is 0.5 * m * v2. When the momentum of the object increases, how does that affect the object's kinetic energy?
kinetic energy increases
Which minimum spanning tree algorithm uses the following greedy choice at each iteration? "Choose the edge (amongst ALL remaining edges in the graph) with the lowest edge cost that does not create a cycle"
kruskals
which handedness defines the 3d cartesian space in the scene tab of the unity editor
left handed
Given a vector v, let w = sv, where s = 0.5. What is the length of w compared to the length of v? Assume that vector v has positive length.
less
Let A be a matrix with dimensions n x k. Let B be a matrix with dimensions k x m. What are the dimensions for AB, i.e. matrix multiplication?
nxm
Which type of projection ensures that parallel lines are still parallel after the projection in ALL cases?
orthographic projection
Which type of projection is also called "Parallel Projection"?
orthographic projection
The flipbook, zoetrope, and thaumatrope approaches make use of what phenomena?
persistence of vision
What type of lens is used in the graphics pipeline presented in the notes?
pinhole
The GameObject class contains a property called transform. Which property of transform would correspond with translation?
position
The angle � (theta) between two vectors is 35 degrees. What is the dot product of these two vectors?
positive
What term describes the repeated use of an object primitive to construct an object in world space?
primitive instancing
What scale factors are used to reflect the 2D point (-2, -3) about the origin to the first quadrant in Cartesian coordinates?
sx = -1, sy = -1
Is the following statement TRUE or FALSE? "Shear is an affine transformation"
true
Is the following statement TRUE or FALSE? A quaternion may be converted to a rotation matrix.
true
What defines the orientation of the camera?
up vector
Which coordinate axis is computed LAST in eye space?
v
When computing the cross product between two vectors, what type of value is the result?
vector
In eye space, what is the name of the area in the scene that is viewable?
view frustrum
You want to apply a shear with factor h in the POSITIVE Y-DIRECTION on 2D vertices, i.e. transform point (x, y) to (x', y'). To define the shear: x' = x. What is the equation for y' ?
y' = y + x * h
Given a connected graph G = (V, E), how many edges will be contained in a spanning tree of G?
|v|-1
