BSP Trees & Rendering: Back-to-Front & Barycentric Techniques - Prof. Juraj Obert, Exams of Computer Graphics

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Juraj Obert

[email protected]

http://graphics.cs.ucf.edu/cap4720/fall2008/

BSP trees revisited

BSP – Binary Space Partitioning

A

B C

BSP construction

p

p

p

p

p

p4 p

p

BSP construction cont.

BuildTree(tree, polygonList)

if (polygonList.count <= 1)

tree.polygons = polygonList[0];

return tree;

tree.splitter = chooseSplitter(polygonList);

foreach polygon P1 in polygonList do classifyPolygon(P1, splitter)

case FRONT: frontList.add(P1);

case BACK: backList.add(P1);

case COINCIDENT: tree.polygons.add(P1);

case SPANNING: splitPolygons(P1, splitter, P1front, P1back);

frontList.add(P1front);

backList.add(P1back);

BuildTree(tree.front, frontList);

BuildTree(tree.back, backList);

Painter’s algorithm

Painter’s Algorithm cont.

How to sort polygons back-to-front?

 Easy in 2D space

 Easy in 3D space if polygons are coplanar

 Not easy if polygons aren’t coplanar

 Difficult if their planes interest

BSP trees can help us

BSP rendering

p

p

p

p

p

p

BSP rendering algorithm

DrawTree(tree, eye) classifyPosition(tree.splitter, eye); case FRONT: DrawTree(tree.back); DrawPolygon(tree.polygons); DrawTree(tree.front); case BACK: DrawTree(tree.front); DrawPolygon(tree.polygons); DrawTree(tree.back); case COINCIDENT: DrawTree(tree.front); DrawTree(tree.back);

Z/Depth buffer revisited

Same resolution as color buffer

 z values from [ 0.0f, 1.0f ]

 z-test

Compare z-value of a pixel already on the screen (zold) and

z-value of a fragment just computed in a fragment shader

(znew)

Pass (znew < zold): new fragment overwrites old pixel

Fail (znew > zold): new fragment is rejected

In OpenGL:

 glEnable

 glDepthFunc

Example

Z-buffer for a simple scene

Shaders

Short programs executed on processing units

inside a GPU

 Vertex/pixel shader units (e.g. 4/16 for GeForce 6800)

 Unified design (e.g. 128 for GeForce 8800 Ultra)

Variety of shading languages

 GLSL (OpenGL Shading Language)

 HLSL (High Level Shading Language)

 Cg (C for Graphics)

Focus now on fragment shaders

Applications of fragment shaders

Graphics:

 Lighting computations

 Texturing

 Shadows

 Color correction

 Tone mapping

 Image processing

GPGPU:

 Wavelet transformations

 Matrix multiplication

 Compression

Vertex shader to fragment shader

“varying” variable type

varying vec4 tri_col;

void main()

tri_col = vec4(…);

Declare and set in vertex shader: (^) Declare and use in frag shader:

varying vec4 tri_col;

void main()

Vertex shader to fragment shader

How does the GPU compute value of tri_color for fragment P?

vertex B

tri_color = vec4(1.0f, 0.0f, 0.0f, 1.0f);

fragment P

vertex C

tri_color = vec4(0.0f, 0.0f, 1.0f, 1.0f);

vertex A

tri_color = vec4(0.0f, 1.0f, 0.0f, 1.0f);

Barycentric coordinates

Given point P, what masses would you assign to

triangle vertices to make P the geometric

centroid of the triangle?

fragment P

vertex A barycentric coordinate u

vertex C barycentric coordinate w

vertex B barycentric coordinate v

Barycentric coordinates cont.

u = Area(PCB) / Area(ACB) v = Area(PAC) / Area(ACB) w = 1 – u – v

Computing area of a triangle:

v 1 = C - P v 2 = B - P

Area(PCB) = 0.5 * || v 1 x v 2 ||

P

vertex A barycentric coordinate u

vertex C barycentric coordinate w

vertex B barycentric coordinate v

Normalized barycentric coordinates: u + v + w = 1.

v 2 v 1

Next class

Lighting