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## PowerPoint Slideshow about 'Frustum Culling in OpenGL' - lane-beard

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How can bounding volume hierarchies help?

Culling Techniques

Fall 2006 revised

Outline

- Introduction
- View Frustum
- Plane Equation
- Frustum Plane Extraction
- Frustum/Point/Sphere Inclusion Tests

Fall 2006 revised

Definition (View Frustum)

- the volume of space that includes everything visible from a given viewpoint
- defined by six planes arranged in the shape of a pyramid with the top chopped off
- If a point is inside this volume then it's in the frustum and it's visible, and vice versa
- Visible here mean potentially visible. It might be behind another point that obscures it, but it's still in the frustum. … the scope of occlusion culling

Fall 2006 revised

View Frustum (cont)

Fall 2006 revised

Definition (Plane)

- Divide the space into two halves; extends to infinity
- any given point is (in front of | behind | on) the plane.
- In R3, a plane is defined by four numbers:
- A plane equation: Ax + By + Cz +D = 0

Fall 2006 revised

Plane Equation

Fall 2006 revised

Normalized Plane Equation

Fall 2006 revised

Frustum Culling

- Idea:
- If object is not in frustum, do not send it through pipeline (it is not visible)
- Wrap the object in a bounding volume; test the bounding volume against frustum (in world coordinate system)
- Sphere, bounding boxes, …
- Tasks:
- Frustum plane extraction
- Inclusion tests for different bounding volumes

Fall 2006 revised

The left plane in clip coordinate:

The corresponding equation in world coordinate:

uy

ux

-1

1

Left

Left Plane (cont)Fall 2006 revised

The right plane in clip coordinate:

The corresponding equation in world coordinate:

Right

uy

ux

-1

1

Right Plane (cont)Fall 2006 revised

Summary

Fall 2006 revised

PointInFrustum Test

- A point in frustumin all 6 halfspaces

The valid sides of all halfspaces are > 0

Fall 2006 revised

uy

ux

-1

1

Left

Signed Distance to Left Plane- Plane equations are further normalized to facilitate distance computation

d<0

Fall 2006 revised

Remarks

- Use bounding spheres
- Can be conservative if the object is slender
- Use hierarchical bounding volume where appropriate (see next page)
- BoxInFrustum:
- complicated and expensive
- AABB: already so
- OBB: more so

Fall 2006 revised

How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

Example (Culling Off: FPS 15.5)

Fall 2006 revised

Example (Culling On: FPS 31.0)

Fall 2006 revised

Similar to building walkthrough

Occlusions in scene are common (culling important)

Geometric database can be huge; preprocessing is required to facilitate smooth viewing

Indoor ScenesFall 2006 revised

Potential visible set (PVS)

only load the rooms that are visible from the current room

Preprocessing for Indoor ScenesFall 2006 revised

Portal Rendering

- only render the other rooms in PVS if the “portal surfaces” are in sight

Fall 2006 revised

the scene is (mostly) static and specified in their world coordinate (the modeling transform is identity)

the viewer navigates around them, changing the viewing transform only

Frustum Culling ScenarioFall 2006 revised

Modelview

Matrix

Viewing

Transform

Model

Transform

world

coordinates

Therefore …I

t

u

s

t = PMs

M : viewing transform

s : world coordinate

Fall 2006 revised

Summary

- Algebraic equation
- Parametric equation
- Vector equation
- Depending on the application, select the most suitable equation
- In/out test
- Projection
- …

Fall 2006 revised

Compute and display the screen-space bounding box of an AABB (axis-aligned bounding box)

Convert world coordinates to clip coordinates, perspective-divide to get window coordinates

Useful in GPU-assisted collision detection applications

Screen-Space Bounding Box (SSBB)Fall 2006 revised

Useful for projective texturing (showing where the projector is)

Useful for illustrating frustum culling

Given [-1,1]3 clip coordinates, determine their corresponding world coordinates to render

Display Viewing FrustumFall 2006 revised

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