ECS175 - Computer Graphics Pipelines and Coordinate Systems

Distinctive Features of Modern GPUs

Massive parallelism, high throughput architecture, dedicated hardware for graphics pipelines, optimized high-performance floating point calculations, memory bandwidth and architecture, CUDA/GPU programming frameworks, energy effieciency for parallel workloads, scalability

Components of computer graphics system

I/O devices, CPU, GPU, Memory, framebuffer

Raster

An array of picture elements

Framebuffer

A region of memory storing pixel data, which may contain multiple buffers like color, depth, and stencil buffers.

Rasterization (scan conversion)

The conversion of geometric entities to pixel colors and locations in the framebuffer.

GPU components

Graphics memory (framebuffer), graphics processor, video controller

Rasterizer

Scan converts each in-view primitive into a set of fragments

Fragment

Holds onto the color, position, and depth of a potential pixel

Framebuffer performance is determined by...

screen resolution, depth, refresh rate

GPUs are used in many applications for its...

parallel processing

Graphics pipeline

vertex processor, clipping and primitive assembly, rasterization, fragment processing

Vertex processor

Transforms vertices in world space into vertices in camera space; Performs transformations and projections;

Clipper and primitive assembler

Assembles primitives from vertices, then clips primitives that are out of view

Fragment processor

Processes fragments to update pixels in framebuffer; Performs tasks like texture combining, per-fragment shading, depth and alpha tests.

Graphics pipeline conversions

scene, geometric primitives, fragments, pixels

Point

a location in space

Vector

a quantity with magnitude and direction

Scalar

a quantity with no locality or direction

Dimension (of a vector space)

max number of linearly independent vectors in vector space

Vector space

A space where vectors and scalars can be combined to create new vectors

Euclidean space

An extension vector space that allows vector measurement; Equipped with inner product providing notion of angle and distance

Affine space

An extension of vector space that includes points; Points can be combined with themselves or vectors to yield vectors or more points respectively

Affine

Preserving the geometry (line and parallelism) of objects (but not necessarily distances)

Linear interpolation between points

(1 - a)*P0 + a*P1

Parametric form of line

P0 + a*V

What’s so good about an affine space?

In an affine space, we can fix a particular reference point to represent all points unambiguously; This reference point is the origin of a coordinate system and together with three coordinate axes, allowing us to locate any point in 3D space defined by the system;

Dot product

Measures the alignment between two vectors; ∑(u_i * v_i) OR |u||v|cos(theta)

Cross product

Gets the vector n orthogonal to two vectors u and v

3D transformation matrix

| | 1×3 |

| 3×3 rotate, scale, reflect, shear | translation |

| ___________________________ | ___________ |

| 1 × 3 perspective TF | scaling |

Basis vectors

linearly independent vectors that can be used to many any vector in the vector space

Coordinate system pipeline

model space, world space, eye space, clip space, normalized device coords, screen space

Transformation pipeline

modeling, viewing, projection, perspective divide, viewport mapping

model space

the model’s coordinate system relative to its center/origin

modeling transform

transforms model space coords to world space coords

viewing transform

transforms world coords to eye/cam space coords

model-view transform

a combo of the modelling and viewing transforms

projection transform

Based on perspective type, field of view, aspect ratio, and near-far clipping planes, maps object from 3D space to 2D screen by projecting everything in visible view volume to canonical view volume

perspective divide

transforms clip space coords into normalized device coords

viewport mapping

transforms 3D normalized device coords into 2D screen space coordinates

homogenous coordinates

a projective coordinate system that allows affine transformations to be represented within one matrix