Section 2 (graphics)

Computer Graphics Using Direct 3D Basics

Outline • Vectors for Direct3D Graphics • Transformations and Matrices • Direct3D 9.0 Rendering Pipeline (The story of a pixel) 2

Outline • Vectors for Direct3D Graphics • Transformations and Matrices • Direct3D 9.0 Rendering Pipeline (The story of a pixel) 3

Vectors • • • • • •

Left-handed Coordinate System Vector addition and subtraction Dot product (Why needed ?) Cross product (Why needed ?) Magnitude Normalization 4

D3DVECTOR Type

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D3DXVECTOR

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D3DXVECTOR (Cont.)

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D3DXVECTOR (Cont.)

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D3DXVECTOR (Cont.) • Direct3D provides utility functions for vectors such as D3DXVec3Length, D3DXVec3Normalize, D3DXVec3Dot, D3DXVec3Cross • Direct3D also provides D3DXVECTOR2 and D3DXVECTOR4 types to represent 2-D and 4D vectors.

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Outline • Vectors for Direct3D Graphics • Transformations and Matrices • Direct3D 9.0 Rendering Pipeline (The story of a pixel) 10

Transformations • The rendering technique used by Direct3D depends on “projecting” 3D objects onto “image plane”.

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Transformations (Cont.) • This needs 3 transformations: – Transforming object points from local to world coordinate system (World Transformation) – Transforming object points from world coordinates to camera-relative coordinates (Camera Transformation) 12

Transformations (Cont.) • This needs 3 transformations: – Transforming object points 3D camera coordinate system to 2D image coordinate system (Projection Transformation)

• In this session, we will focus on world transformation. 13

Transformations (Cont.) • Many transformations (e.g. rotation, scaling, translation, skew) can be represented by a set of linear equations • x` = a0x + b0y + c0z + d0 • y` = a1x + b1y + c1z + d1 • z` = a2x + b2y + c2z + d2

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Transformations (Cont.) • This set can be represented by a single matrix equation [x` y` z` 1] = a 0 a 1 a2 a3 [x y z 1][ b0 b1 b2 b3 ] c0 c1 c2 c3 d0 d1 d2 d3 15

Transformations (Cont.) • Example: Translation +3 along x-axis [x` y` z` 1] = 1000 [x y z 1][ 0 1 0 0 ] 0010 3001

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Transformations (Cont.) • Matrix representation allows for easy combination of transformations: – xAB = x(AB) = (xA)B

• Applying the transformation AB is equivalent to applying A then B • Transformations are combined by multiplying corresponding matrices 17

Transformations (Cont.) • More on transformations and transformation matrices will be studied in the lectures.

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D3DMATRIX

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D3DXMATRIX • D3DXMATRIX extends D3DMATRIX providing access functions and overloaded operators.

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D3DXMATRIX • There are utility functions to perform common matrix operations such as D3DXMatrixIdentity, D3DXmatrixTranspose and D3DXMatrixInverse • There are also functions to construct common transformation matrices such as D3DXMatrixTranslation, D3DXMatrixRotationX and D3DXMatrixScaling

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D3DXMATRIX • D3DXTransformCoord applies a transformation matrix to a D3DXVector • D3DXTransformNormal applies a transformation matrix to a D3DXVector without the 4th row. Useful when the vector represents a direction rather than a location (e.g. normal vector) (Why ?) 22

Mid-way Summary • 3D Graphics use vectors and vector operations. • Transformations of vectors can be represented by matrices. • D3DXVECTOR and D3DXMATRIX classes and associated functions provide a handy matrix toolset. 23

Outline • Vectors for Direct3D Graphics • Transformations and Matrices • Direct3D 9.0 Rendering Pipeline (The story of a pixel) 24

Why study the pipeline ??

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Direct3D 9.0 Pipeline

[Image from MSDN] 26

Direct3D 9.0 Pipeline (Cont.) • Vertex Data – Untransformed model vertices stored in memory buffers [Vertex Buffer]

• Primitive Data – Geometric primitives (lines, triangles, polygons ... etc) refer to vertices using indices [Index Buffers]

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Direct3D 9.0 Pipeline (Cont.) • Tessellation – Extract vertices from higher-order primitives

• Vertex Processing – Transformation – Per-vertex Lighting

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Direct3D 9.0 Pipeline (Cont.) • Geometry Processing – Clipping – Backface Culling – Rasterization

• Pixel Processing – Given geometry and texture data, determine final pixel color (final for the primitive not the image) 29

Direct3D 9.0 Pipeline (Cont.) • Pixel Rendering – Determine final pixel color to be output to the image plane (rendering target) • Object occlusion (Depth test) • Blending • Stencil test, Alpha test

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Direct3D 9.0 Pipeline (Cont.) • This was the fixed rendering pipeline • The programmable rendering pipeline allows you to override vertex and pixel processing stages using vertex and pixel shaders

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Summary • We have overviewed the DirectX pipeline and its stages. • Meanwhile we encountered important terms such as vertex, pixel, primitive, texture, light, shaders. • Also, we have got insight on an important stage in the pipeline which is vertex transformation. 32

Any Questions ??

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