Introduction to Computer Graphics (Glossary)

HSV color

A color specified by three numbers giving the hue, saturation, and value of the component. The hue represents the basic color. The saturation is the purity of the color, with a saturation value of zero producing a shade of gray, that is a color with no actual hue at all. The value represents the brightness of the color, with a value of zero giving black. (Value is also called brightness, and the name HSB is sometimes used instead of HSV.)

drawing program

A computer program for creating images using vector-style graphics, where the user creates the image by specifying shapes that make up the image and their attributes.

Blender

A free and open source 3D modeling and animation program.

camera

In 3D computer graphics, an object that combines the projection and viewing transforms into an abstraction that imitates a physical camera or eye.

back face

One of the two sides of a polygon in 3D. A polygon has two sides. One is taken to be the front face, and the other is the back face. In OpenGL, the difference is determined by the order in which the vertices of the polygon are enumerated. The default is that, seen from the back, the vertices are enumerated in clockwise order around the polygon.

front face

One of the two sides of a polygon in 3D. A polygon has two sides. One is taken to be the front face, and the other is the back face. In OpenGL, the difference is determined by the order in which the vertices of the polygon are enumerated. The default is that, seen from the front, the vertices are enumerated in counterclockwise order around the polygon.

GLSL

OpenGL Shader Language, the programming languauge that is used to write shader programs for use with OpenGL.

color gamut

The color gamut of a display device, such as a printer or computer screen, is the set of colors can be displayed by the device.

GUI

(Graphical User Interface.) A user interface for a program where the user interacts with the program using components such as windows, menus, buttons, and text-input boxes.

indexed face set

(IFS). A data structure that represents a polyhedron or polygonal mesh. The data structure includes a numbered list of vertices and a list of faces. A face is specified by listing the indices of the vertices of the face; that is, a face is given as a list of numbers where each number is an index into the list of vertices.

JOGL

A Java implementation of OpenGL. JOGL is very complicated, since it attempts to support all versions of OpenGL in one programming system. JOGL integrates seamlessly with Java's Swing and AWT graphics.

HTML canvas

A canvas element on a web page. The canvas appears as a rectangular area on the page. The JavaScript programming language can use a canvas element as a drawing surface. HTML is a language for specifying the content of a web page. JavaScript is the programming language for web pages. The canvas element supports a 2D graphics API. In many browsers, it also supports the 3D graphics API, WebGL.

indexed color

A color scheme in which colors are selected from a limited palette of colors. For example, if the palette contains 256 colors, then a color can be specified by an eight-bit integer, giving its position, or index, in the list of colors.

HSL color

A color specified by three numbers giving the hue, saturation, and lightness of the component. The HSL color model is similar to the HSV color model. The main difference is that in HSL, pure spectral colors occur when L=0.5, while in HSV, they occur when V=1.

convex

A convex geometric shape has the property that whenever two points are contained in the shape, then the line segment between those two points is entirely contained in the shape.

barycentric coordinates

A coordinate system on a triangle in which a point is written as a linear combination of the vertices of the triangle, that is, a*A+b*B+c*C, where A, B, and C are the vertices and a, b, and c are numbers. Any point in the triangle can be written in this form where the coefficients a, b, and c have values in the range 0 to 1 and a+b+c is equal to 1.

geometric transform

A coordinate transformation; that is, a function that can be applied to each of the points in a geometric object to produce a new object. Common transforms include scaling, rotation, and translation.

fixed-function pipeline

A graphics processing pipeline with a fixed set of processing stages that cannot be modified by a programmer. Data for an image passes through a sequence of processing stages, with the image as the end product. The sequence is called a "pipeline." With a fixed-function pipeline, the programmer can enable and disable stages and set options that control the processing but cannot add to the functionality.

double buffering

A graphics technique in which an image is drawn off-screen, in a region of memory called an off-screen buffer or "back buffer." When the image is drawn, it can be copied to the buffer that represents the contents of the screen, which is also known as the "front buffer." In true double buffering, the image doesn't have to be copied; instead, the buffers can be "swapped" so that the back buffer becomes the front buffer, and the front buffer becomes the back buffer.

intensity of a light source

A light source emits light at various wavelengths. The intensity of a light at a given wavelength is the amount of energy in the light at that wavelength. The total intensity of the light is its total energy at all wavelengths. The color of a light is determined by its intensities at all wavelengths.

directional light

A light source whose light rays are parallel, all arriving from the same direction. Can be considered to be a light source at an effectively infinite distance. Also called a "sun," since the Sun is an example of a directional light source.

flat shading

A lighting computation for the faces of a polygon or polygonal mesh that uses the same normal vector at each point in the polygon, giving the polygon a flat or faceted appearance.

display list

A list of graphics primitives and attributes which can be traversed to create all or part of an image. Display lists were used in some early vector-graphics hardware. They were also available in traditional OpenGL.

emission color

A material property that represents color that is intrinsic to a surface, rather than coming from light from other sources that is reflected by the surface. Emission color can make the object look like it is glowing, but it does not illuminate other objects. Emission color is often called "emissive color."

ambient color

A material property that represents the proportion of ambient light in the environment that is reflected by a surface.

diffuse color

A material property that represents the proportion of incident light that is reflected diffusely from a surface.

deferred shading

A multi-pass rendering technique where a first pass processes the geometry and saves relevant information such as transformed coordinates, normal vectors, and material properties. The data can be stored in textures, which are called "geometry buffers" or "G-buffers" in this context. Lighting and other effects can then be computed in additional passes, using the pre-computed information from the geometry buffers instead of re-computing it for each pass.

gradient

A pattern of color produced by assigning colors to certain reference points and computing color for other points by interpolating or extrapolating colors from the reference points. The effect is a color progression along line segments between reference points. Different rules for extending the colors beyond those lines produce different types of gradient, such as linear gradients and radial gradients.

control point

A point that does not lie on the curve but that is used to help control the shape of the curve. For example, a control point for a Bezier curve segment is used to specify the tangent vector (direction and speed) of the curve at an endpoint.

JavaScript

A programming language for web pages. JavaScript code on a web page is executed by a web browser that displays the page, and it can interact with the contents of the web page and with the user. There are JavaScript APIs for 2D and for 3D graphics

attribute

A property, such as color, of a graphical object. An image can be specified by the geometric shapes that it contains, together with their attributes.

frame buffer

A region of memory that contains color data for a digital image. Most often refers to the memory containing the image that appears on the computer's screen.

depth buffer

A region of memory that stores the information needed for the depth test in 3D graphics, that is, a depth value for each pixel in the image. Also called the "z-buffer."

ambient occlusion

A rendering technique that takes into account the fact that ambient light will illuminate different surfaces to varying extents, depending on the degree to which ambient light is blocked, or "occluded," from reaching each surface by other geometry in the scene. Ambient occlusion is an improvement on basic ambient lighting, but it is not an actual physical phenomenon.

animation

A sequence of images that, when displayed quickly one after the other, will produce the impression of continuous motion or change. The term animation also refers to the process of creating such image sequences.

fragment shader

A shader program that will be executed once for each pixel in a primitive. A fragment shader must compute a color for the pixel, or discard it. Fragment shaders are also called pixel shaders.

Bezier curve

A smooth curve between two points defined by parametric polynomial equations. A cubic Bezier curve segment is defined by its two endpoints P1 and P2 and by two control points C1 and C2. The tangent to the curve (its direction and speed) at P1 is given by the line from P1 to C1. The tangent vector to the curve at P2 is given by the line from C2 to P2. A quadratic Bezier curve is defined by its two endpoints and a single control point C. The tangent at each endpoint is the line between that endpoint and C.

depth test

A solution to the hidden surface problem that involves keeping track of the depth, or distance from the viewer, of the object currently visible at each pixel in the image. When a new object is drawn at a pixel, the depth of the new object is compared to the depth of the current object to decide which one is closer to the viewer. The advantage of the depth test is that objects can be rendered in any order. A disadvantage is that only a limited range of depths can be represented in the image.

Bresenham's line algorithm

A specific algorithm for deciding which pixels to color to represent a geometric line segment, using only integer arithmetic. The algorithm can be implemented very efficiently in computer hardware

anaglyph stereo

A technique for combining stereographic images of a scene, one for the left eye and one for the right eye, into a single image. Typically, the image for the left eye is drawn using only shades of red, and the image for the right eye contains only blue and green color components. The 3D effect can be seen by viewing the combined image through red/cyan glasses, which allow each eye to see only the image that is intended for that eye.

anisotropic filtering

A technique for more accurate sampling of texture images, in the case where a pixel on the surface that is being textured corresponds to a non-rectangular region in the texture. Anisotropic filtering is available as an optional extension in WebGL.

extrusion

A technique for producing a solid from a 2D shape by moving the shape along a curve in 3D. The solid is the set of points through which the shape passes as it moves along the curve. The most common case is moving the shape along a line segment that is perpendicular to the plane that contains the shape. In practice, in computer graphics, the object that is produced by extrusion is just the surface of the extruded solid.

antialiasing

A technique used to reduce the jagged or "staircase" appearance of diagonal lines, text, and other shapes that are drawn using pixels. When a pixel is only partly covered by a geometric shape, then the color of the pixel is a blend of the color of the shape and the color of the background, with the degree of blending depending on the fraction of the pixel that is covered by the geometric shape.

cubemap texture

A texture made up of six images, one for each of the directions positive x, negative x, positive y, negative y, positive z, and negative z. The images are intended to include everything that can be seen from a given point. Cubemap textures are used for environment mapping and skyboxes.

identity transform

A transform that has no effect on its argument. For example, the identity transform in 2D is given by the formula I(x,y) = (x,y). The identity transform I has the property that if T is any transform, then I followed by T is the same as T, and T followed by I is the same as T.

Euclidean transform

A transform that preserves distances and angles. A Euclidean transform represents a "rigid motion." That is, the transform of an object is an exact copy of the object, with the same size and shape. Any Euclidean transform can be represented as a composition of rotations and translations.

affine transform

A transform that preserves parallel lines. That is, when the transform is applied to a pair of lines that are parallel, then the resulting transformed lines are also parallel. An affine transform, T, has the property that the transform of the line segment between a point (x1,y1) and a point (x2,y2) is the line between the points T(x1,y1) and T(x2,y2). Effectively, the transform of a line segment can be computed just by transforming its two endpoints. This makes affine transforms very efficient for computer graphics. Any affine transform can be represented as a composition of rotations, translations, and scalings.

frustum

A truncated pyramid; that is, a pyramid from which the top has been cut off. In OpenGL 1.1, the view volume for a perspective projection is a frustum.

cross product

A vector product of two 3D vectors. The cross product of v and w is a vector that is perpendicular to both v and w and whose length is equal to the absolute value of the sine of the angle between v and w. If v=(x,y,z) and w=(a,b,c), then their cross product is the vector (yc-zb,za-xc,xb-ya).

coordinate system

A way of assigning numerical coordinates to geometric points. In two dimensions, each point corresponds to a pair of numbers. In three dimensions, each point corresponds to a triple of numbers.

homogeneous coordinates

A way of representing n-dimensional vectors as (n+1)-dimensional vectors where two (n+1) vectors represent the same n-dimensional vector if they differ by a scalar multiple. In 3D, for example, if w is not zero, then the homogeneous coordinates (x,y,z,w) are equivalent to homogeneous coordinates (x/w,y/w,z/w,1), since they differ by multiplication by the scalar w. Both sets of coordinates represent the 3D vector (x/w,y/w,z/w)

environment mapping

A way of simulating mirror-like reflection from the surface of an object. The environment that is to be reflected from the surface is represented as a cubemap texture. To determine what point in the texture is visible at a given point on the object, a ray from the viewpoint is reflected from the surface point, and the reflected ray is intersected with the texture cube. Environment mapping is also called reflection mapping.

color model

A way of specifying colors numerically. Each color that can represented in a color model is assigned one or more numerical component values. An example is the RGB color model, where a color is specified by three numbers giving the red, green, and blue components of the color.

directed acyclic graph

Also called a "dag." A linked data structure in which there are no cycles. That is, it is not possible to find a sequence of nodes where each node links to the next and the last node links back to the first.

alpha color component

An extra component (that is, one of the numbers that are used to specify a color) in a color model that is not part of the actual color specification. The alpha component is extra information. It is most often used to specify the degree of transparency of a color.

image texture

An image that is applied to a surface as a texture, so that it looks at if the image is "painted" onto the surface.

Eclipse

An integrated development environment for writing programs in Java (and other programming languages). Eclipse is a free program that can be downloaded from http://eclipse.org.

glMatrix

An open-source JavaScript library for vector and matrix math in two and three dimensions.

API

Application Programming Interface. A collection of related classes, functions, constants, etc., for performing some task. An API is an "interface" in the sense that it can be used without understanding how its functionality is actually implemented.

BSDF

Bidirectional Scattering Distribution Function. A generalization of the idea of "material" in 3D graphics. A BSDF gives the probability that a light ray that arrives at point of space from one direction will leave that point heading in a another direction. The probability is a function of the two directions, the point, and the wavelength of the light. Once kind of scattering is reflection of light from a surface. For that case, the term BRDF (Bidirectional Reflectance Distribution Function) is used.

CSS

Cascading Style Sheets. A language that is used for specifying the style, or presentation, of the content of web pages. CSS can control things like colors, backgrounds, fonts, shadows, borders, and the size and position of elements of the page.

column-major order

Column-by-column ordering of the elements of a two-dimensional matrix; that is, an ordering that starts with the elements in the first column, followed by the elements in the second column, and so on. Column-major order is used for matrices in OpenGL and GLSL.

geometric modeling

Creating a scene by specifying the geometric objects contained in the scene, together with geometric transforms to be applied to them and attributes that determine their appearance.

hierarchical modeling

Creating complex geometric models in a hierarchical fashion, starting with geometric primitives, combining them into components that can then be further combined into more complex components, and so on.

ambient light

Directionless light that exists in an environment but does not seem to come from a particular source in the environment. An approximation for light that has been reflected so many times that its original source can't be identified. Ambient light illuminates all objects in a scene equally.

DOM

Document Object Model. A specification for representing a web page (and other kinds of structured document) as a tree-like data structure. Can also refer to the data structure itself, as in "the DOM for this web page." A web page can be modified dynamically by manipulating its DOM, using the JavaScript programming language.

filling a shape

Drawing the interior of a shape, by coloring the pixels that lie inside the shape. Filling does not apply to shapes, such as lines, that have no interior.

Euler angles

Express the rotation of an object in its own coordinate system, given as individual rotations about the x, y, and z axes in that coordinate system. The cumulative effect of rotations about the three coordinate axes depends on the order in which the rotations are applied.

geometric primitive

Geometric objects in a graphics system, such as OpenGL, that are not made up of simpler objects. Examples in OpenGL include points, lines, and triangles, but the set of available primitives depends on the graphics system. (Note that as the term is used in OpenGL, a single primitive can be made up of many points, line segments, or triangles.)

inverse transform

Given a transform T, the inverse transform of T is a transform that reverses the operation of T. For example, for a 2D transform, for R to be the inverse of T means that R(T(x,y)) = (x,y). Scaling by 0.5 is the inverse of scaling by 2. Translation by (-3,5) is the inverse of translation by (3,-5). Not every transform has an inverse. For example, scaling by a factor of zero has no inverse.

interpolation

Given values for some quantity at certain reference points, computing a value for that quantity at other points by some kind of averaging applied to the values at the reference points.

GPU

Graphics Processing Unit, a computer hardware component that performs graphical computations that create and manipulate images. Operations such as drawing a line on the screen or rendering a 3D image are done in the GPU, which is optimized to perform such operations very quickly.

HTML

HyperText Markup Language. A language that is used for specifying the content of web pages. An HTML document is made up of text, along with "elements" for adding other content, such as images, and for defining the structure of the document. Because of nesting of elements, the document can be represented by a tree-like data structure.

invariant qualifier

In GLSL, a modifier that ensures that when the same expression is used to compute the value of a variable in two different shaders, the value will be the same in both shaders. This can be important for multi-pass algorithms, where several shader programs are applied in succession to render one image.

global ambient intensity

In OpenGL, ambient light that is present in the environment independent of any light source. Total ambient light is the sum of the global ambient light plus the ambient light intensity of each enabled light source.

color buffer

In OpenGL, the region of memory that holds the color data for the image. It acts as the drawing surface where images are rendered.

framebuffer

In WebGL, a data structure that organizes the buffers for rendering an image, possibly including a color buffer, a depth buffer, and a stencil buffer. A WebGL graphics context has a default framebuffer for on-screen rendering, and additional framebuffers can be created for off-screen rendering.

depth mask

In WebGL, a setting that controls whether depth values are written to the depth buffer during rendering. When the depth mask is set to false, the depth value is discarded and the depth buffer is unchanged.

color mask

In WebGL, a setting that determines which "channels" in the color buffer are written during rendering. The channels are the RGBA color components red, green, blue, and alpha. A color mask consists of four boolean values, one for each channel. A false value prevents any change from being made to the corresponding color component in the color buffer.

abstract class

In object-oriented programming, a class that is meant to be used only as a basis for subclasses. Objects can be created from the subclasses, but not from the abstract class itself. The purpose of an abstract class is to define the properties and behaviors that all of its subclasses have in common.

constructor

In object-oriented programming, a subroutine that is used to create objects. A constructor for a class creates and initializes objects belonging to that class. (JavaScript, which does not have classes as such, does have constructors, so that a constructor in effect defines a class.)

IOR

Index of Refraction. A property of a medium, such as air or glass, that transmits light. The refraction, or bending, of light rays that pass from one medium to another depends on the ratio of the IORs of the two media. The index of refraction of a medium depends on the speed of light in that medium.

color component

One of the numbers used in a color model to specify a color. For example, in the RGB color model, a color is specified by three color components representing the amounts of red, green, and blue in the color.

grayscale

Refers to a color scheme or image in which each color is a shade of gray (where the term "shade of gray" here includes black and white). Typically, 256 shades of gray are used. Grayscale is also called "monochrome."

attenuation

Refers to the way that illumination from a point light or spot light decreases with distance from the light. Physically, illumination should decrease with the square of the distance, but computer graphics often uses a linear attenuation with distance, or no attenuation at at all.

diffuse reflection

Reflection of incident light in all directions from a surface, so that diffuse illumination of a surface is visible to all viewers, independent of the viewer's position.

axis of rotation

Rotation in 3D space is rotation about a line, which is called the axis of rotation. The axis of rotation remains fixed, while everything else moves in circles around the axis.

CPU

The Central Processing Unit in a computer, the component that actually executes programs. The CPU reads machine language instructions from the computer's memory and carries them out.

GLUT

The OpenGL Utility Toolkit. A platform-independent library for writing OpenGL applications. OpenGL does not include support for windows or events. GLUT adds such support. It also has functions for drawing 3D shapes such as spheres and polyhedra (not to mention a teapot). GLUT is written in the C programming language and is used with the C API for OpenGL. However, many GLUT functions are also available in JOGL, the Java API for OpenGL. A newer, and somewhat improved, version of the toolkit named "FreeGLUT" is commonly used in place of the original version.

GLU

The OpenGL Utility library. Defines several functions for use with older versions of OpenGL, including gluPerspective and gluLookAt. Not to be confused with GLUT. GLU is a standard part of OpenGL.

eye coordinates

The coordinate system on 3D space defined by the viewer. In eye coordinates in OpenGL 1.1, the viewer is located at the origin, looking in the direction of the negative z-axis, with the positive y-axis pointing upwards, and the positive x-axis pointing to the right. The modelview transformation maps objects into the eye coordinate system, and the projection transform maps eye coordinates to clip coordinates.

device coordinates

The coordinate system used on a display device or rendered image, often using pixels as the unit of measure.

clip coordinates

The default coordinate system in OpenGL. The projection transform maps the 3D scene to clip coordinates. The rendered image will show the contents of the cube in the clip coordinate system that contains x, y, and z values in the range from -1 to 1; anything outside that range is "clipped" away.

dot product

The dot product of two vectors is the sum of the products of corresponding coordinates. For 3D vectors v=(x,y,z) and w=(a,b,c), the dot product of v and w is x*a+y*b+z*c. The dot product is equal to the cosine of the angle between the vectors, divided by the product of their lengths.

identity matrix

The n-by-n identity matrix is an n-by-n matrix which has ones on the diagonal and zeros elsewhere. Multiplication of any matrix B by the identity matrix, in either order, leaves B unchanged. Multiplication of an n-dimensional vector by the n-by-n identity matrix leaves the vector unchanged; that is, the identity matrix is the matrix for the identity transformation.

hidden surface problem

The problem in 3D graphics of deciding which object is visible at each pixel in an image. When one object is behind another object from the point of view of the viewer, only the front object should appear in the image. A rendering algorithm for 3D graphics must satisfy this constraint. Algorithms that solve the hidden surface problem include the painter's algorithm and the depth test algorithm.

aspect ratio

The ratio of the width, w, of a rectangle to the height, h, of the rectangle, expressed either as a ratio w:h or as a fraction w/h.

bumpmapping

Using a texture to modify the normal vectors on a surface, to give the appearance of variations in height without actually modifying the geometry of the surface.

alpha blending

Using the alpha component of a color to blend the color with a background color, when the color is drawn over the background color. That is, the new color of a pixel is obtained by blending the drawing color with the current color, with the degree of blending depending on the alpha component of the drawing color. Alpha blending is most commonly used to simulate transparency.

attribute variable

Variables that represent input to the vertex shader in a programmable graphics pipeline. An attribute variable can take on a different value for each vertex in a primitive.