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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

Frustum Culling in OpenGL

Ref: MarkMoley.com

Fall 2006 revised

culling techniques
Culling Techniques

Fall 2006 revised

outline
Outline
  • Introduction
    • View Frustum
    • Plane Equation
  • Frustum Plane Extraction
  • Frustum/Point/Sphere Inclusion Tests

Fall 2006 revised

definition view frustum
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
View Frustum (cont)

Fall 2006 revised

definition plane
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
Plane Equation

Fall 2006 revised

normalized plane equation
Normalized Plane Equation

Fall 2006 revised

frustum culling
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

frustum plane extraction
u

s

t

M

P

Frustum Plane Extraction
  • The rendering pipeline:

Fall 2006 revised

rendering pipeline cont
u

s

t

M

P

Rendering Pipeline (cont)

c : product of PM

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

Fall 2006 revised

frustum plane extraction left
uy

ux

-1

1

Left

Frustum Plane Extraction (Left)

Fall 2006 revised

left plane cont
The left plane in clip coordinate:

The corresponding equation in world coordinate:

uy

ux

-1

1

Left

Left Plane (cont)

Fall 2006 revised

frustum plane extraction right
uy

ux

-1

1

Right

Frustum Plane Extraction (Right)

Fall 2006 revised

right plane cont
The right plane in clip coordinate:

The corresponding equation in world coordinate:

Right

uy

ux

-1

1

Right Plane (cont)

Fall 2006 revised

summary
Summary

Fall 2006 revised

pointinfrustum test
PointInFrustum Test
  • A point in frustumin all 6 halfspaces

The valid sides of all halfspaces are > 0

Fall 2006 revised

sphereinfrustum test
SphereInFrustum Test

p

p

PointInOffsetFrustum Test

Minkowski sum of sphere and frustum

Fall 2006 revised

minkowski sum
Minkowski Sum

Coordinate dependent!

Fall 2006 revised

signed distance to left plane
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
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
How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

how can bounding volume hierarchies help1
How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

how can bounding volume hierarchies help2
How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

how can bounding volume hierarchies help3
How can bounding volume hierarchies help?

View-frustum culling

Ray-tracing

Collision detection

Fall 2006 revised

epilogue

Epilogue

Portal rendering

World coordinates?!

Plane representation in R3

Fall 2006 revised

indoor scenes
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

preprocessing for indoor scenes
Potential visible set (PVS)

only load the rooms that are visible from the current room

Preprocessing for Indoor Scenes

Fall 2006 revised

slide31
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
Portal Rendering
  • only render the other rooms in PVS if the “portal surfaces” are in sight

Fall 2006 revised

earlier we said
u

s

t

M

P

Earlier, we said…

But aren’t slocal coordinates?

Fall 2006 revised

recall pipeline
Modelview

Matrix

Viewing

Transform

Model

Transform

world

coordinates

Recall Pipeline…

Fall 2006 revised

frustum culling scenario
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

therefore
Modelview

Matrix

Viewing

Transform

Model

Transform

world

coordinates

Therefore …

I

t

u

s

t = PMs

M : viewing transform

s : world coordinate

Fall 2006 revised

verification
x–z+10

L

R

–x–z+10

X

Z

Verification

Fall 2006 revised

supplement representing a plane in r 3
Supplement: Representing a Plane in R3

x: pivot variable

Fall 2006 revised

plane in r 3 cont
Plane in R3 (cont)

n

x

p

Fall 2006 revised

summary1
Summary
  • Algebraic equation
  • Parametric equation
  • Vector equation
  • Depending on the application, select the most suitable equation
    • In/out test
    • Projection

Fall 2006 revised

screen space bounding box ssbb
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

display viewing frustum
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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