terrain collision detection

TerrainTerrain&&

Collision DetectionCollision DetectionCollision DetectionCollision Detection

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Both of topics are very gameBoth of topics are very game--typetype--oriented dataoriented data

Introduction (1/2)Introduction (1/2)Both of topics are very gameBoth of topics are very game typetype oriented dataoriented dataTerrainTerrain

For visual purposeFor visual purposeGround / Building / Static models / Dynamic modelsGround / Building / Static models / Dynamic models

For terrain followingFor terrain followingP l hP l hPolygon meshPolygon meshGridsGrids

For path findingFor path findingFor path findingFor path findingPolygon meshPolygon meshGridsGrids

Terrain followingTerrain followingMake a 3D entity (character or model) walking Make a 3D entity (character or model) walking onon terrainterrain

P th fi diP th fi diPath findingPath findingFind a “shortest” path to walk before movingFind a “shortest” path to walk before movingWill be taught in Game AI section.Will be taught in Game AI section.

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Will be taught in Game AI section.Will be taught in Game AI section.A* algorithmA* algorithm

Collision detectionCollision detection

Introduction (2/2)Introduction (2/2)Collision detectionCollision detection

The basic solution for collision detection is solving the intersection of a ray The basic solution for collision detection is solving the intersection of a ray with a plane.with a plane.We will introduce :We will introduce :We will introduce :We will introduce :

Containment testContainment testSeparating axisSeparating axis

Collision avoidanceCollision avoidanceWill be introduced at Steer behavior in Game AI sectionWill be introduced at Steer behavior in Game AI section

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GridGrid

Terrain FormatsTerrain FormatsGridGrid

2D2DQuadtreeQuadtree

H i h H i h Height mapHeight mapProcedural height mapProcedural height mapUsing noise function to generate the heightUsing noise function to generate the heightg g gg g g

ROAMROAM

Perlin Noise

RRealeal--time time OOptimally ptimally AAdapting dapting MMesheseshesTriangular meshTriangular mesh

Procedurally generatedProcedurally generatedProcedurally generatedProcedurally generatedCreated by artistsCreated by artists

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2D grid map2D grid map

Grid MapGrid Map2D grid map2D grid map

Rectangular or Hexagonal gridsRectangular or Hexagonal gridsAttributesAttributes

HeightHeightWalkable or notWalkable or notT t tt IDT t tt IDTexture pattern IDTexture pattern ID

Step look terrainStep look terrainpp

ApplicationApplication2D games2D games2D games2D games3D games with god view3D games with god view

2D tile2D tile--based game terrainbased game terrain

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Almost as same as 2D grid map but :"Almost as same as 2D grid map but :"

Height MapHeight MapAlmost as same as 2D grid map but :Almost as same as 2D grid map but :

Height on grid vertexHeight on grid vertexOnly height is savedOnly height is saved

Top view

Regular gridRegular gridIrregular grid but structuredIrregular grid but structured

ApplicationApplicationAs the base data structure for ROAM terrainAs the base data structure for ROAM terrainWater simulationWater simulation

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RealReal--time optimally adapting meshtime optimally adapting mesh

ROAMROAMRealReal time optimally adapting meshtime optimally adapting mesh

http://www.llnl.gov/graphics/ROAM/http://www.llnl.gov/graphics/ROAM/

ApplicationApplicationApplicationApplicationFlyFly--simulationsimulation

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Use quad tree to construct the levelUse quad tree to construct the level--ofof--detail of terraindetail of terrain

Chunked LOD TerrainChunked LOD TerrainUse quad tree to construct the levelUse quad tree to construct the level ofof detail of terraindetail of terrain

A A quad tree for LODquad tree for LOD

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Possibly the most popular way for 3D gamesPossibly the most popular way for 3D games

Triangular MeshTriangular MeshPossibly the most popular way for 3D gamesPossibly the most popular way for 3D games

GeneralGeneralCan be created by artistsCan be created by artists

MultipleMultiple--layered terrain issuelayered terrain issue

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hh

Triangular Coordinate SystemTriangular Coordinate System

hhaa

AAcc pp

((xxaa,y,yaa,z,zaa))

hhhhbb

AAaa

ccAAbb

pp

((xxbb,y,ybb,z,zbb))

hhccAA AA AA

((xxcc,y,ycc,z,zcc))

h = hh = haa + + hhbb + + hhcc

where A =where A = AA ++ AAbb + A+ A

AAaa AAbb AAcc

AA AA AA

where A where A AAaa + + AAbb + A+ Acc

If (If (AAaa < 0 || < 0 || AAbb < 0 || A< 0 || Acc < 0) than< 0) thanthe point is outside the trianglethe point is outside the trianglethe point is outside the trianglethe point is outside the triangle

“Triangular Coordinate System”“Triangular Coordinate System”“B t i C di t S t ”

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“Barycentric Coordinate System”

Triangle Area Triangle Area –– 2D2D

Area of a triangle in 2D

xa yaa yaA = ½ xb yb

xc ycx yxa ya

= ½ (xa*yb + xb*yc + xc*ya – xb*ya – xc*yb – xa*yc)

(xa,ya,za)

(x y z )(xb,yb,zb)

11(xc,yc,zc)

Triangle Area Triangle Area –– 3D3D

Area of a triangle in 3D A = ½ (N. Sum(Pi1 cross Pi2))where (i1, i2) = (a,b), (b,c), (c,a)

float GmArea3(float *x0, float *x1, float *x2, float *n){

float area len sum1 sum2 sum0;float area, len, sum1, sum2, sum0;len = (float) sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]) * 2.0f;

/* find s m of cross prod cts *//* find sum of cross products */sum0 = x1[1] * (-x0[2] + x2[2]) + x2[1] * (-x1[2] + x0[2]) +

x0[1] * (-x2[2] + x1[2]);sum1 = x1[2] * (-x0[0] + x2[0]) + x2[2] * (-x1[0] + x0[0]) +

x0[2] * (-x2[0] + x1[0]);sum2 = x1[0] * (-x0[1] + x2[1]) + x2[0] * (-x1[1] + x0[1]) +

x0[0] * (-x2[1] + x1[1]);

/* find the area */

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d t e a ea return = (sum0 * n[0] + sum1 * n[1] + sum2 * n[2]) / len;

}

Terrain followingTerrain following

Triangular Coordinate System Triangular Coordinate System -- ApplicationApplicationTerrain followingTerrain following

Interpolating the height of arbitrary point within the triangleInterpolating the height of arbitrary point within the triangleHit testHit test

Intersection of a ray from camera to a screen position with a Intersection of a ray from camera to a screen position with a triangletriangle

Ray castRay castRay castRay castIntersection of a ray with a triangleIntersection of a ray with a triangle

Collision detectionCollision detectionCollision detectionCollision detectionIntersectionIntersection

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Ray Cast Ray Cast –– The RayThe RayCast a ray to calculate the intersection of the ray with modelsCast a ray to calculate the intersection of the ray with modelsCast a ray to calculate the intersection of the ray with modelsCast a ray to calculate the intersection of the ray with modelsUse parametric equation for a rayUse parametric equation for a ray

x = xx = x00 + (x+ (x11 –– xx00) t) ty = yy = y00 + (y+ (y11 –– yy00) t, t = 0,) t, t = 0,

(( ) t) t{{ 88

z = zz = z00 + (z+ (z11 –– zz00) t ) t {{

When t = 0, the ray is on the start point (xWhen t = 0, the ray is on the start point (x00,y,y00,z,z00))Only the t Only the t ≥≥ 0 is the answer candidate0 is the answer candidateThe smallest positive t is the answerThe smallest positive t is the answer

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Ray Cast Ray Cast –– The PlaneThe PlaneEach triangle in the 3D models has its plane equationEach triangle in the 3D models has its plane equationEach triangle in the 3D models has its plane equation.Each triangle in the 3D models has its plane equation.UUse se ax + by + cz + d = 0ax + by + cz + d = 0 as the plane equation.as the plane equation.((a, b, c)a, b, c) is the plane normal vector.is the plane normal vector.(( ))|d||d| is the distance of the plane to origin.is the distance of the plane to origin.Substitute the ray equation into the plane.Substitute the ray equation into the plane.Solve the Solve the tt to find the intersect point.to find the intersect point.

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Solve the terrain height for the object to stand onSolve the terrain height for the object to stand on

Terrain Following Using Triangular MeshTerrain Following Using Triangular MeshSolve the terrain height for the object to stand on.Solve the terrain height for the object to stand on.

Use the triangular coordinate system (p. 154)Use the triangular coordinate system (p. 154)Find the next neighboring triangleFind the next neighboring triangle

HalfHalf--edge data structureedge data structure

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Create cohesive relationship between triangles using “half edge”Create cohesive relationship between triangles using “half edge”

HalfHalf--edge (1/2)edge (1/2)

Create cohesive relationship between triangles using “half edge”Create cohesive relationship between triangles using “half edge”UUse halfse half--edge table to search the neighboring trianglesedge table to search the neighboring triangles

Edge = two halves

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struct HE edge

HalfHalf--edge (2/2)edge (2/2)struct HE_edge{

HE_vert* vert; // vertex at the end of the half-edgeHE_edge* pair; // oppositely oriented adjacent half-edgeHE f * f // f h h lf d b dHE_face* face; // face the half-edge bordersHE_edge* next; // next half-edge around the face

};

struct HE_vert{

fl t float x;float y;float z;HE edge* edge; // one of the half-edgesHE_edge edge; // one of the half edges

// emantating from the vertex};

t t HE fstruct HE_face{

HE_edge* edge; // one of the half-edges bordering the face};

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};

http://www.flipcode.com/tutorials/tut_halfedge.shtml

Ray castRay cast

IntersectionIntersectionRay castRay castContainment testContainment testSeparating axesSeparating axes

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2D Containment Test2D Containment Test

Intersection = 1, inside

Intersection = 2, outside

(x y ) Intersection = 0, outside

Trick : Parametric equation for a ray which is parallel to the x axis

(x0, y0)

Trick : Parametric equation for a ray which is parallel to the x-axis

x = x0 + t t 0 { 8y = y0 , t = 0, { 8

“if the No of intersection is odd the point is inside

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if the No. of intersection is odd, the point is inside,otherwise, is outside”

3D Containment Test3D Containment TestSame as the 2D containment testSame as the 2D containment testSame as the 2D containment testSame as the 2D containment test

“if the No of intersection is odd the point is insideif the No. of intersection is odd, the point is inside,otherwise, is outside”

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Separating AxesSeparating AxesFFor convex objects onlyor convex objects onlyFFor convex objects onlyor convex objects onlyIIf there is existing an axis (2D) or a plane (3D) to separate two convex f there is existing an axis (2D) or a plane (3D) to separate two convex objects, these two objects are not intersected.objects, these two objects are not intersected.

How ?How ?Project the vertices of each object on the axis/plane that is Project the vertices of each object on the axis/plane that is perpendicular to axis/plane we are going to findperpendicular to axis/plane we are going to findperpendicular to axis/plane we are going to find.perpendicular to axis/plane we are going to find.Get the extreme of the projection area of each object.Get the extreme of the projection area of each object.

IIf the projection are of these two object are not overlapped the f the projection are of these two object are not overlapped the

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IIf the projection are of these two object are not overlapped, the f the projection are of these two object are not overlapped, the two objects are not intersected.two objects are not intersected.

Separating Axes Algorithm for Convex Polyhedra (1/3)Separating Axes Algorithm for Convex Polyhedra (1/3)

Bool TestIntersect(ConvexPolyhedron C0, ConvexPolyhedron C1){

// test faces of C0 for separationfor (i = 0; i < C0 GetFaceCount(); i++) {for (i = 0; i < C0.GetFaceCount(); i++) {

D = C0.GetNormal(i);ComputeInterval(C0, D, min0, max0);ComputeInterval(C1, D, min1, max1);if (max1 < min0 || max0 < min1) return false;

}

// test faces of C1 for separation// test faces of C1 for separationfor (i = 0; i < C1.GetFaceCount(); i++) {

D = C1.GetNormal(i);ComputeInterval(C0, D, min0, max0);ComputeInterval(C1, D, min1, max1);if (max1 < min0 || max0 < min1) return false;

}

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// test cross products of pairs of edgesfor (i = 0; i < C0.GetEdgeCount(); i++) {

for (j = 0; j < C1.GetEdgeCount(); j++) {D = Cross(C0 GetEdge(i) C1 GetEdge(j));D = Cross(C0.GetEdge(i), C1.GetEdge(j));ComputeInterval(C0, D, min0, max0);ComputeInterval(C1, D, min1, max1);if (max1 < min0 || max0 < min1) return false;

}}

return true;return true;}

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void ComputeInterval(ConvexPolyhedron C, Vector D,double &min, double &max)

{min = Dot(D C GetVertex(0));min = Dot(D, C.GetVertex(0));max = min;for (i = 1; i < C.GetVertexCount(); i++) {

value = Dot(D, C.GetVertex(i));if (value < min) min = value;else if (value > max) max = value;

}}}

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Use bounding volume to improve the performanceUse bounding volume to improve the performance

Summary for Collision DetectionSummary for Collision DetectionUse bounding volume to improve the performanceUse bounding volume to improve the performance

Cylinder volume for charactersCylinder volume for charactersObjectObject--oriented bounding box (OBB) or bounding sphere for 3D modelsoriented bounding box (OBB) or bounding sphere for 3D models

Collision detection when the object/character is movingCollision detection when the object/character is movingVery game type orientedVery game type oriented“Collision Avoidance” “Collision Avoidance” vsvs “Collision Detection”“Collision Detection”Tricks! Tricks! Tricks!Tricks! Tricks! Tricks!

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terrain collision detection

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