Frustum Culling in OpenGL Ref: MarkMoley.com Fall 2006 revised

Culling Techniques Fall 2006 revised

Outline Introduction Frustum Plane Extraction 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: Tasks: 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 The rendering pipeline: P M s u t In frustum culling, s is usually a point on BV, in world coordinate Fall 2006 revised

Rendering Pipeline (cont) M s u t c : product of PM In OpenGL,clip volume is [-1,1]3 Fall 2006 revised

Frustum Plane Extraction (Left) ux uy -1 1 Left Fall 2006 revised

Left Plane (cont) The left plane in clip coordinate: ux uy -1 1 Left The left plane in clip coordinate: The corresponding equation in world coordinate: Fall 2006 revised

Frustum Plane Extraction (Right) ux uy -1 1 Right Fall 2006 revised

Right Plane (cont) The right plane in clip coordinate: ux uy -1 1 Right The right plane in clip coordinate: The corresponding equation in world coordinate: Fall 2006 revised

Summary Fall 2006 revised

The valid sides of all halfspaces are > 0 PointInFrustum Test A point in frustumin all 6 halfspaces The valid sides of all halfspaces are > 0 Fall 2006 revised

SphereInFrustum Test PointInOffsetFrustum Test Minkowski sum of sphere and frustum Fall 2006 revised

Minkowski Sum Coordinate dependent! Fall 2006 revised

Signed Distance to Left Plane Plane equations are further normalized to facilitate distance computation ux uy -1 1 Left 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

Portal rendering World coordinates?! Plane representation in R3 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 Fall 2006 revised

Preprocessing for Indoor Scenes Potential visible set (PVS) only load the rooms that are visible from the current room Fall 2006 revised

Portal Rendering M R K L Ki B C E 1 2 3 4 5 6 7 8 M B 1 4 E 2 C 7 3 6 Fall 2006 revised Ki

Portal Rendering only render the other rooms in PVS if the “portal surfaces” are in sight Fall 2006 revised

But aren’t s local coordinates? Earlier, we said… P M s u t But aren’t s local coordinates? Fall 2006 revised

Recall Pipeline… Modelview Matrix Fall 2006 revised world coordinates Transform Viewing Modelview Matrix world coordinates 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 Fall 2006 revised

Therefore … I t u s t = PMs M : viewing transform s : world coordinate Model Transform Viewing Modelview Matrix world coordinates I t u s t = PMs M : viewing transform s : world coordinate Fall 2006 revised

Verification L R X Z x–z+10 –x–z+10 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

Screen-Space Bounding Box (SSBB) Useful in GPU-assisted collision detection applications 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 normalized device coordinate (and then window coordinates) 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 Fall 2006 revised