Cylinder Collision. Reddy Sambavaram 9/07/2007

Transcription

1 Cylinder Collision Reddy Sambavaram 9/07/2007

2 Cylinder Collision PART 1: collision algorithms. PART 2: What did it mean to add a new collision primitive to the engine and tools? What had to change? What was the process?

3 PART 1: Primitives/Collision types Primitives: Sphere Capsule OOBB Tri mesh skinned and not skinned Cylinder

4 Part 1: Misc notes Started as game-play/design request to accurately represent and interact with certain objects (like trash cans ) Difficult problem to solve (cheaply) mainly because of geometric discontinuity at end caps Very little literature which covers all queries and do them efficiently for our needs (most cite problems and recommend just use capsules in the end).

5 Part1: Queries to support Line vs Cylinder (projectiles use these a lot) Swept Sphere vs Cylinder (mover code uses these a lot) We are interested in the closest intersection from the start in above queries Following queries come in 2 flavors List type query (Do prims intersect or not) Full type query (If prims intersect what is the best pt of intersection, depth, normal..) Sphere <-> Cylinder Capsule <-> Cylinder OOBB <-> Cylinder Tri-Mesh <-> Cylinder Cylinder - Cylinder

6 Line vs Cylinder Ref: Intersect SegmentCylinder page 197 (Real time collision detection by Christer Ericson) Parametrically solve for line intersecting infinite cylinder and check if it hits end caps. Line A->B and Cylinder center end points P->Q X = A + t(b-a); T = (X-P); T = T T.(Q-P); (component perpendicular to Q-P); T.T = r^2; (would result in quadratic equation in t) If eqn has 1 or more roots Based on the distance from P if < 0 or > Q-P we further test against the end cap of interest (circle plane vs line test)

7 We do it in max 2 stages Swept-sphere vs cylinder Stage 1) Cast Swept-Sphere vs cylinder into Line vs augmented-cylinder

8 Swept-sphere vs cylinder (contd) If (stage1) returns false then abort (no intersection) Else we can have false positives at the corners. We can check if the intersection point is in the corner cheaply by looking at its offset from the midpoint of the cylinder (half point on the cylinder axis) If not corner then return the result. Else go to stage 2)

9 Swept-sphere vs cylinder (contd) Stage 2) case where stage one yielded a corner intersection Based on the intersection pt from stage 1 we can clamp it to the radius and axis of the non-augmented cylinder to get the corner pt on the cylinder. Also, note that this corner point is the point of intersection for the swept sphere if it actually intersects the cylinder (no space to prove this here). We take advantage of the above fact and transform the problem into a sphere with center at the corner pt and radius of the input swept sphere s radius and swept-line check. If this intersects we have a valid intersection and corner pt is the pt of contact.

10 Sphere vs Cylinder Compute the axial and radial offset of the sphere center with respect Cylinder center ( o )

11 Sphere vs Cylinder contd Seems like a bunch of branches but most of them are made branchless on SPU as either side of the branch is not doing much work.

12 Capsule vs cylinder Did not pursue the thought of transforming the problem to line vs augmented cylinder (with axis and radius incremented by capsule s radius) as we are interested in best pt of intersection not the closest from one end (like swept sphere) Took advantage of the already implemented good closest pts between line segments algorithm

13 Capsule vs cylinder (contd)

14 OOBB vs Cylinder (one of the toughest ones as geometric discontinuities on both primitives) Transform Cylinder into OOBB space (less error prone and can visualize better) 1)ClosestPointsLineVsAABB(cyl_center0, cyl_center1, aabb_center, aabb_radii); Above gives Pcyl and Paabb (two closest points) If ( Dist (Pcyl, Paabb) > cyl_radius) abort; (if capsule cant intersect then cylinder wont) 2) cyl_center = (cyl_center0 + cyl_center1)/2; Let OPaabb be vector from cyl_center to Paabb OPaabb can be decomposed to OPabbb-per (component perpendicular to cylinder axis) OPabbb-para (component parallel to cylinder axis) if (Legnth(OPabbb-per) > cyl_radius) abort; (as it implies cylinder is outside AABB) if (Length(OPaabb-per) < Dist(cyl_center, dyl_center0) then Paabb is the pt of intersection 3) if (Length(OPaabb-para) > Dist(cyl_center, cyl_center0) then we check all the 3 axis planes pasing through Paabb with respect the cylinder end cap at Pcyl

15 OOBB vs Cylinder (contd)

16 OOBB vs Cylinder (contd) To check each plane passing through Paabb and cylinder end cap If blue ray (computed by taking the perpendicular compoenet of vector from AABB center to Pcyl) through Pcyl intersects the plane and the point of intersection lies with in the AABB s boundaries with in the plane then we have valid intersection. This point is what we are looking for. All you need is first valid intersection (if Paabb is on edges all will give same results)

17 Tri - Cylinder Modified ("A Fast Triangle-Triangle intersection test" by Tomas Moller) to suit for cylinder end tri test 0) Let cyl_center0 be origin and cyl_center1 is on z axis 3) ComputeClosestPointsLineVsTri(cyl_axis, tri) Results Pcyl, Ptri. If (Ptri.z < axis_len && PTri.z > 0) if (Dist(PCyl, Ptri) < cyl_rad) PTri is the intersection pt; If (Tri normal is parallel to axis) if (Dist(Pcyl, Ptri) > 0) abort else PTri is our pt of interest 10) Now we need to check end cap with the tri when end cap is not parallel to tri (used above mentioned reference for this) Compute the line of intersection between end cap and tri. Clip it by the end cap circle, clip it further by the tri. Closest pt on the clipped lines to the end_cap center is the pt of interest. Compute the distance from end_cap to all the 3 verts. If all the vert_distances are positive then abort; Sort the verts by their distances and select 2 edges which go from +ve to ve regards distance with end cap; Get the line which intersects the two planes: Compute line of intersection between end_cap and tri plane s direction by crossing their normals. Compute the a pt of intersection by taking the biggest axis of the tri normal (apart from z axis). Computes the intersection pts of the above line with the 2 selected edges of the tri. Now compute the closest pt on the line joining the intersection pts with respect to end_cap center and with in the radius.

18 Cylinder vs Cylinder Eberly proposed a list query using separating axis method but the number of axis were so many that he decides it is getting expensive and recommends to use capsules instead Following is a geometric solution in the scaled cylinder axis space If axes are parallel handle it separately (not so interesting so skipping it)

19 Cylinder vs Cylinder (contd)

20 Cylinder vs Cylinder (contd) Now define new space where x and z are as shown in pervious slide Now scale y axis by the factor (R1+R2)/(R1Cos + R2) so that the augmented cylinder crossection becomes circle again Now transform the Cyl1_center0 and Cyl1_center1 into the new scaled space and run the Else LinevsCylinder check if (doesn t intersect) abort) check for false positives and if none found return true False positives if above returns an intersection

21 Cylinder vs cylinder (contd) If both cyl1_center0 and cyl_center1 are on positive side of either of the 2 false-positive planes as shown we abort. Actually we do the false positive test before we do the actual scaled_cylinder space linevs-cylinder check (as it is computationally cheap and early out is good) SIMD on SPU makes all the above scaling and choosing the planes and axes much cheaper than it appears (Seems much faster than separating axis method) Regards point of intersection we give a pt of intersection not always the best for now.

22 Feed back Please mail with any bugs in the approach or if you have any ideas or thoughts to tackle any of the queries in a different/modified way

23 PART2 (How did we add a cylinder into our pipeline) PUTTING IT IN ENGINE Cylinder foot print is the same as capsule except for how we interpret the ends as end_caps rather than hemi-spheres Extended the dimension of the primitives in engine with CylinderPrimitivetype Implemented all the queries and add to the switch statements in each of the quiries likes (Line vs prim, sweptsphere vs prim, Sphere vs Prim, Obb vs Prim) Added CylinderQuery functions API for all query types (list, non-list, deferred, non-deferred..) Initially added Broad phase Cylinder support but after talking to Jonny we decided it is not worth it and rout cylinder queries to use Capsule for broad phase and cylinder for narrow Added debug cylinder prim (very handy tool during implementation of the queries and debugging). This is the first thing added in the task and started of hijacking a capsule to write all the run time queries before maya support was in.

24 PART2 (How did we add a cylinder into our pipeline) ADDING A CYLINDER AND GETTING IT INTO THE GAME In maya a new locator for cylinder is supported (By Andy B), which is functionally similar to capsules where the 2 ends can be parented to joints to bind them Modified mobybuilder to out put cylinder prims (much similar to capsules) Cylinders are not taken into account in physics yet so cylinders cant have physics. For now we can have stationery cylinder in game with which we can interact. Ratchet can move around it, stand on it. Cylinder is still expensive compared to capsule so please use capsules if you can get away with it.

25 QUESTIONS?