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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: In frustum culling, s is usually a point on BV, in world coordinate 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 frustumin 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+10**L R –x–z+10 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 normalized device coordinate (and then 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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