# Frustum Culling in OpenGL - PowerPoint PPT Presentation

1 / 42

Frustum Culling in OpenGL. Ref: MarkMoley.com. Culling Techniques. Outline. Introduction View Frustum Plane Equation Frustum Plane Extraction Frustum/Point/Sphere Inclusion Tests. Definition (View Frustum). the volume of space that includes everything visible from a given viewpoint

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Frustum Culling in OpenGL

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Frustum Culling in OpenGL

Ref: MarkMoley.com

Fall 2006 revised

### 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, …

• Frustum plane extraction

• Inclusion tests for different bounding volumes

Fall 2006 revised

u

s

t

M

P

### Frustum Plane Extraction

• The rendering pipeline:

Fall 2006 revised

u

s

t

M

P

### Rendering Pipeline (cont)

c : product of PM

In OpenGL,clip volume is [-1,1]3

Fall 2006 revised

uy

ux

-1

1

Left

### Frustum Plane Extraction (Left)

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

uy

ux

-1

1

Right

### Frustum Plane Extraction (Right)

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 frustumin all 6 halfspaces

The valid sides of all halfspaces are > 0

Fall 2006 revised

### SphereInFrustum Test

p

p

PointInOffsetFrustum Test

Minkowski sum of sphere and frustum

Fall 2006 revised

### Minkowski Sum

Coordinate dependent!

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

• 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

### How can bounding volume hierarchies help?

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

## Epilogue

Portal rendering

World coordinates?!

Plane representation in R3

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 Scenes

Fall 2006 revised

Potential visible set (PVS)

only load the rooms that are visible from the current room

### Preprocessing for Indoor Scenes

Fall 2006 revised

1

7

2

4

3

6

5

E

M

B

8

L

C

R

Ki

K

M

Portal Rendering

B

1

4

E

2

C

7

3

6

5

L

8

R

K

Fall 2006 revised

Ki

### Portal Rendering

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

Fall 2006 revised

u

s

t

M

P

### Earlier, we said…

But aren’t slocal coordinates?

Fall 2006 revised

Modelview

Matrix

Viewing

Transform

Model

Transform

world

coordinates

### Recall Pipeline…

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 Scenario

Fall 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

x–z+10

L

R

–x–z+10

X

Z

### Verification

Fall 2006 revised

### Supplement: Representing a Plane in R3

x: pivot variable

Fall 2006 revised

### Plane in R3 (cont)

n

x

p

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 Frustum

Fall 2006 revised