cps 511 final

Graphics Pipeline Diagram

A flowchart showing how 3D data becomes a 2D image (modeling → viewing → projection → clipping → rasterizing → shading → output).

Modeling Stage

Places objects into the world using transforms like scale, rotate, translate.

Viewing Stage

Moves and orients the camera so the world is seen from the correct viewpoint.

Projection Stage

Converts 3D view into a 2D image using orthographic or perspective projection.

Clipping Stage

Removes geometry outside the camera frustum so only visible objects are processed.

Rasterization Stage

Converts triangles into fragments/pixels.

Shading Stage

Computes lighting and color for each visible fragment.

Output Stage

Displays the final processed pixels onto the screen.

Object Coordinates

Local coordinate system of an individual model before being placed in the world.

World Coordinates

Shared scene coordinate system where all objects exist together.

Camera/Eye Coordinates

Coordinates expressed relative to the camera’s position and orientation.

Clip Coordinates

4D coordinates after projection but before perspective division used for clipping.

NDC Coordinates

Standardized cube (−1 to 1) representing visible space after perspective division.

Screen Coordinates

Pixel coordinates after mapping NDC to the viewport.

Transformations Between Coordinate Systems

Matrices that convert points from object → world → eye → clip → NDC → screen.

Rasterization

The process of turning triangles into pixel-sized fragments.

Lighting/Shading

Calculating brightness and color per fragment based on lights and materials.

Visible Surface Determination

Algorithms deciding which surfaces are in front.

Rasterization Diagram

A triangle filled pixel-by-pixel.

Lighting Diagram

Shows light direction, normal, and reflection.

Visibility Diagram

Shows occlusion using depth.

Fixed Pipeline Stages

Non-programmable GPU stages such as clipping, rasterizing, depth testing.

Translation Matrix

A matrix that moves an object in x, y, and z.

Rotation Matrix

A matrix that rotates an object around an axis.

Scaling Matrix

A matrix that enlarges or shrinks an object.

Combining Transformations

Applying transforms in sequence where the order affects the result.

Transformation Sequence

Ordered list of transforms like scale → rotate → translate.

Camera Position

The eye location in world coordinates.

Look-at Point

The point the camera is aimed at.

Up Vector

The direction that defines “up” for the camera.

Camera Basis (u,v,w)

Camera’s right, up, and backward axes used to build the view matrix.

gluLookAt

Function that constructs the viewing transformation matrix.

Viewing Formula V = R T

Viewing transformation equals rotation times translation.

Ortho Matrix Derivation

Built using translate, scale, and reflect operations to normalize the view volume.

Similar Triangles Projection

Reason distant objects appear smaller based on triangle proportions.

Homogeneous Coordinates

4D representation needed for translation and perspective in matrix form.

W Component

Stores depth information for perspective foreshortening.

Perspective Division

Dividing x,y,z by w to apply perspective effects.

Perspective Projection Matrix

Built from scaling, shearing, and translating to form a frustum.

Global Illumination

Lighting model including indirect light bounces.

Local Illumination

Lighting based only on direct light.

Ambient Term

Constant background light applied everywhere.

Diffuse Term

Light depending on angle between normal and light direction.

Specular Term

Shiny highlight depending on viewer and reflection vector.

Phong Dot Products

n·l and r·v calculations determining diffuse and specular lighting.

Phong Diagram

Diagram showing normal, light, view, and reflection directions.

Calculator Use

Needed for Phong calculations when numbers are provided.

Flat Shading

Lighting once per polygon producing faceted surfaces.

Gouraud Shading

Lighting per vertex then interpolated across the polygon.

Phong Shading

Lighting per fragment giving smooth, accurate results.

BRDF

Function describing how surfaces reflect light in different directions.

Texture Mapping Basics

Applying a 2D image onto a 3D object using texture coordinates.

Texture Coordinate Systems

Texture space (s,t), parametric space (u,v), object space, screen space.

Two-Part Mapping

Mapping texture to an intermediate shape then onto a complex object.

Environment Mapping

Using cube or sphere maps to simulate reflections.

Bump Mapping

Fake bumps by modifying surface normals using a texture.

Minification Problem

Too many texels per pixel causing aliasing.

Magnification Problem

Too few texels per pixel causing pixelation.

Mipmapping

Multiple resolutions of textures used to reduce aliasing at distance.

Anisotropic Filtering

Improves texture quality at steep viewing angles.

Cohen–Sutherland Clipping

Line clipping using region outcodes.

Sutherland–Hodgman Clipping

Polygon clipping by clipping against each plane sequentially.

DDA Algorithm

Line rasterization using incremental steps.

Bresenham’s Algorithm

Efficient line rasterization choosing nearest integer pixel.

Triangle Rasterization

Determining which pixels lie inside a triangle.

Inside/Outside Tests

Using edge functions or barycentric coordinates to test containment.

Polygon Rasterization

Filling polygons by splitting into triangles or scanning.

Tile-Based Rasterization

Dividing the screen into small tiles for efficient rasterization.

Viewport Transform Matrix

Converts NDC coordinates to actual screen pixel positions.

Back-Face Culling

Removing triangles facing away from the camera.

Painter’s Algorithm

Draw far objects first then near ones.

Z-Buffer Algorithm

Keeps the closest fragment by comparing depth values.

Depth Non-Linearity

Z precision is higher near the camera and lower far away.

Anti-Aliasing Basics

Techniques for reducing jagged edges.

Primitive Assembly

Combining vertices into triangles or lines.

View-Volume Clipping

Removing geometry outside the canonical view volume.

Perspective Division Stage

Converts clip coordinates into NDC by dividing by w.

Viewport Transformation Stage

Converts NDC to screen coordinates.

Rasterization Stage

Converts primitives into fragments for shading.

Interpolated Attributes

Values like depth, color, and texcoords interpolated across triangles.

1/w Interpolation

Required for correct perspective texture mapping and depth interpolation.

Programmable Pipeline Stages

Vertex and fragment shaders that can run user-defined code.

Fixed Pipeline Stages

Stages that cannot be programmed (clip, rasterize, depth test).

Vertex Shader

Processes each vertex and outputs clip-space position and varyings.

Vertex Shader Inputs

Position, normal, texcoord, and other per-vertex attributes.

Vertex Shader Outputs

Clip-space position and interpolated varyings.

Fragment Shader

Computes final per-pixel color using interpolated data.

Fragment Shader Inputs

Interpolated varyings like color, texcoords, normals.

Fragment Shader Outputs

Final pixel color written to the framebuffer.

Uniform Variables

Constant values used by all shader invocations (lights, matrices, etc.).

Varying/In-Out Variables

Data passed from vertex to fragment shader via interpolation.

Rasterizer Interpolation

Hardware computes how varyings change across a triangle.

Per-Fragment Phong

Phong lighting computed in the fragment shader for accuracy.

Eye-Space Position in Shaders

Vertex shader passes eye-space coordinates for lighting math.

Normals in Shaders

Vertex shader outputs normals for interpolation and fragment lighting.

Ray Tracing Algorithm

Simulates rays to compute lighting, shadows, reflections, and refractions.

Primary Rays

Rays cast from the camera through each pixel.

Secondary Rays

Reflection, shadow, and refraction rays spawned after intersections.

Ray Tracing Diagram

Illustration of rays hitting surfaces and bouncing.

Ray Tracing Pseudocode

Step-by-step outline of casting rays and computing color recursively.