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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

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Frustum Culling in OpenGL

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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, …

  • Tasks:

    • 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

    • 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


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


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