/// <summary>
/// 通过轴分离算法得到bodyA和bodyB的碰撞点
/// </summary>
/// <param name="contacts"></param>
/// <param name="bodyA"></param>
/// <param name="bodyB"></param>
/// <returns></returns>
public static int CollideTest(Contact[] contacts, Body bodyA, Body bodyB)
{
// Setup
Vec2 hA = bodyA.m_size * 0.5f;//half size
Vec2 hB = bodyB.m_size * 0.5f;
Vec2 posA = bodyA.m_position;
Vec2 posB = bodyB.m_position;
Mat22 RotA = new Mat22(bodyA.m_rotation);
Mat22 RotB = new Mat22(bodyB.m_rotation);
//对于二维旋转矩阵，矩阵的转置等于矩阵的逆
Mat22 RotAT = RotA.Transpose();
Mat22 RotBT = RotB.Transpose();
Vec2 dp = posB - posA; //全局坐标系中，由BodyA指向BodyB的向量
Vec2 dA = RotAT * dp; //BodyA的本地坐标系中，由BodyA指向BodyB的向量
Vec2 dB = RotBT * dp; //BodyB的本地坐标系中，由BodyA指向BodyB的向量
Mat22 C = RotAT * RotB;
Mat22 absC = C.Abs();
Mat22 absCT = absC.Transpose();
//确定不相交，提前退出的情形
// Box A faces
//absC*hB会得到B在A的本地坐标系中的轴对齐外接矩形的halfSize
//DebugDraw.Instance.DrawBox(bodyB.m_position, absC * hB * 2, 0, Color.gray);
Vec2 faceA = dA.Abs() - hA - absC * hB;
if (faceA.x > 0.0f || faceA.y > 0.0f)
{
return(0);
}
// Box B faces
//absCT * hA会得到A在B的本地坐标系中的轴对齐外接矩形的halfSize
Vec2 faceB = dB.Abs() - absCT * hA - hB;
if (faceB.x > 0.0f || faceB.y > 0.0f)
{
return(0);
}
//Step 1
// Find best axis
//寻找最小分离轴
Axis axis;
float separation;
Vec2 normal;
// Box A faces
axis = Axis.FACE_A_X;
separation = faceA.x;
//B在A的右方，分离法线是A的X轴方向，由A指向B
//或者B在A的左方，分离法线是A的-X轴方向，由A指向B
normal = dA.x > 0.0f ? RotA.col1 : -RotA.col1;
//const float relativeTol = 0.95f;
//const float absoluteTol = 0.01f;
if (faceA.y > separation)
//if (faceA.y > relativeTol * separation + absoluteTol * hA.y)
{
axis = Axis.FACE_A_Y;
separation = faceA.y;
//B在A的上方，分离法线是A的Y轴方向，由A指向B
//或者B在A的下方，分离法线是A的-Y轴方向，由A指向B
normal = dA.y > 0.0f ? RotA.col2 : -RotA.col2;
}
// Box B faces
if (faceB.x > separation)
//if (faceB.x > relativeTol * separation + absoluteTol * hB.x)
{
axis = Axis.FACE_B_X;
separation = faceB.x;
//B在A的右方，分离法线是B的X轴方向，由A指向B
//或者B在A的左方，分离法线是A的-X轴方向，由A指向B
normal = dB.x > 0.0f ? RotB.col1 : -RotB.col1;
}
if (faceB.y > separation)
//if (faceB.y > relativeTol * separation + absoluteTol * hB.y)
{
axis = Axis.FACE_B_Y;
separation = faceB.y;
//B在A的上方，分离法线是B的Y轴方向，由A指向B
//或者B在A的下方，分离法线是B的-Y轴方向，由A指向B
normal = dB.y > 0.0f ? RotB.col2 : -RotB.col2;
}
// Step 2
// Setup clipping plane data based on the separating axis
//根据最小分离轴，决定了一个是referenceBox,另一个是incidentBox
//获取incident上的碰撞边的数据
//由referenceBox指向incidnetBox的法线
Vec2 frontNormal = new Vec2();
//垂直于frontNormal的方向
Vec2 sideNormal = new Vec2();
//incident上的碰撞边数据
ClipVertex[] incidentEdge = new ClipVertex[2];
//为了支持将IncidentBox的碰撞边根据referenceBox sideNormal方向上的两条边裁剪的数据
float front = 0; //refenceBox的frontNormal方向上的边上的点在frontNormal方向上的投影长度
float negSide = 0; //refenceBox的sideNormal方向上的边上的点在sideNormal方向上的投影长度
float posSide = 0; //refenceBox的-sideNormal方向上的边上的点在-sideNormal方向上的投影长度
//ReferenceBox的两条裁剪边编号
EdgeNumbers negEdge = EdgeNumbers.NO_EDGE;
EdgeNumbers posEdge = EdgeNumbers.NO_EDGE;
// Compute the clipping lines and the line segment to be clipped.
switch (axis)
{
case Axis.FACE_A_X:
{
frontNormal = normal;
front = Vec2.Dot(posA, frontNormal) + hA.x;
sideNormal = RotA.col2;
float side = Vec2.Dot(posA, sideNormal);
negSide = -side + hA.y;
posSide = side + hA.y;
negEdge = EdgeNumbers.EDGE3;
posEdge = EdgeNumbers.EDGE1;
ComputeIncidentEdge(out incidentEdge, hB, posB, RotB, frontNormal);
}
break;
case Axis.FACE_A_Y:
{
frontNormal = normal;
front = Vec2.Dot(posA, frontNormal) + hA.y;
sideNormal = RotA.col1;
float side = Vec2.Dot(posA, sideNormal);
negSide = -side + hA.x;
posSide = side + hA.x;
negEdge = EdgeNumbers.EDGE2;
posEdge = EdgeNumbers.EDGE4;
ComputeIncidentEdge(out incidentEdge, hB, posB, RotB, frontNormal);
}
break;
case Axis.FACE_B_X:
{
frontNormal = -normal;
front = Vec2.Dot(posB, frontNormal) + hB.x;
sideNormal = RotB.col2;
float side = Vec2.Dot(posB, sideNormal);
negSide = -side + hB.y;
posSide = side + hB.y;
negEdge = EdgeNumbers.EDGE3;
posEdge = EdgeNumbers.EDGE1;
ComputeIncidentEdge(out incidentEdge, hA, posA, RotA, frontNormal);
}
break;
case Axis.FACE_B_Y:
{
frontNormal = -normal;
front = Vec2.Dot(posB, frontNormal) + hB.y;
sideNormal = RotB.col1;
float side = Vec2.Dot(posB, sideNormal);
negSide = -side + hB.x;
posSide = side + hB.x;
negEdge = EdgeNumbers.EDGE2;
posEdge = EdgeNumbers.EDGE4;
ComputeIncidentEdge(out incidentEdge, hA, posA, RotA, frontNormal);
}
break;
}
foreach (var clipVertex in incidentEdge)
{
//DebugDraw.Instance.DrawPoint(clipVertex.v, new Color(1,0,0,0.1f));
}
//Step 3
// clip other face with 5 box planes (1 face plane, 4 edge planes)
//将incidentBox碰撞边数据根据referenceBox的两个裁剪边进行裁剪
ClipVertex[] clipPoints1 = new ClipVertex[2];
ClipVertex[] clipPoints2 = new ClipVertex[2];
int np;
// Clip to negative box side 1
np = ClipSegmentToLine(clipPoints1, incidentEdge, -sideNormal, negSide, negEdge);
if (np < 2)
{
return(0);
}
// Clip to positive box side 1
np = ClipSegmentToLine(clipPoints2, clipPoints1, sideNormal, posSide, posEdge);
if (np < 2)
{
return(0);
}
foreach (var clipVertex in clipPoints2)
{
//DebugDraw.Instance.DrawPoint(clipVertex.v, new Color(1, 0, 0, 0.5f));
}
// Now clipPoints2 contains the clipping points.
// Due to roundoff, it is possible that clipping removes all points.
int numContacts = 0;
for (int i = 0; i < 2; ++i)
{
separation = Vec2.Dot(frontNormal, clipPoints2[i].v) - front;
if (separation <= 0)
{
var contact = contacts[numContacts];
contact.m_separation = separation; //是一个负数
contact.m_normal = normal; //由BodyA指向BodyB
// slide contact point onto reference face (easy to cull)
//接触点位于参考Box的表面
contact.m_position = clipPoints2[i].v - frontNormal * separation;
contact.m_feature = clipPoints2[i].feature;
if (axis == Axis.FACE_B_X || axis == Axis.FACE_B_Y)
{
Flip(ref contact.m_feature);
}
contacts[numContacts] = contact;
++numContacts;
}
}
return(numContacts);
}
/// <summary>
/// 返回incident box的碰撞边的顶点,顶点设置顺序保证是逆时针
/// </summary>
/// <param name="clipVertices">返回的incident box的碰撞边的顶点</param>
/// <param name="size">incident box的尺寸</param>
/// <param name="pos">incident box的位置</param>
/// <param name="rot">incident box的旋转</param>
/// <param name="normal">指向incident box的碰撞法线</param>
static void ComputeIncidentEdge(out ClipVertex[] clipVertices, Vec2 size, Vec2 pos, Mat22 rot, Vec2 normal)
{
clipVertices = new ClipVertex[2];
//将碰撞法线转换到incident box的本地坐标系
Mat22 RotT = rot.Transpose();
Vec2 n = -(RotT * normal);
Vec2 nAbs = n.Abs();
//todo 貌似有bug,如果不是正方形
if (nAbs.x > nAbs.y)
{
if (MathUtils.Sign(n.x) > 0)
{
//边4
clipVertices[0].v.Set(size.x, -size.y);
clipVertices[0].feature.inEdge2 = (char)EdgeNumbers.EDGE3;
clipVertices[0].feature.outEdge2 = (char)EdgeNumbers.EDGE4;
clipVertices[1].v.Set(size.x, size.y);
clipVertices[1].feature.inEdge2 = (char)EdgeNumbers.EDGE4;
clipVertices[1].feature.outEdge2 = (char)EdgeNumbers.EDGE1;
}
else
{
//边2
clipVertices[0].v.Set(-size.x, size.y);
clipVertices[0].feature.inEdge2 = (char)EdgeNumbers.EDGE1;
clipVertices[0].feature.outEdge2 = (char)EdgeNumbers.EDGE2;
clipVertices[1].v.Set(-size.x, -size.y);
clipVertices[1].feature.inEdge2 = (char)EdgeNumbers.EDGE2;
clipVertices[1].feature.outEdge2 = (char)EdgeNumbers.EDGE3;
}
}
else
{
if (MathUtils.Sign(n.y) > 0)
{
//边1
clipVertices[0].v.Set(size.x, size.y);
clipVertices[0].feature.inEdge2 = (char)EdgeNumbers.EDGE4;
clipVertices[0].feature.outEdge2 = (char)EdgeNumbers.EDGE1;
clipVertices[1].v.Set(-size.x, size.y);
clipVertices[1].feature.inEdge2 = (char)EdgeNumbers.EDGE1;
clipVertices[1].feature.outEdge2 = (char)EdgeNumbers.EDGE2;
}
else
{
//边3
clipVertices[0].v.Set(-size.x, -size.y);
clipVertices[0].feature.inEdge2 = (char)EdgeNumbers.EDGE2;
clipVertices[0].feature.outEdge2 = (char)EdgeNumbers.EDGE3;
clipVertices[1].v.Set(size.x, -size.y);
clipVertices[1].feature.inEdge2 = (char)EdgeNumbers.EDGE3;
clipVertices[1].feature.outEdge2 = (char)EdgeNumbers.EDGE4;
}
}
//转换到世界坐标系
clipVertices[0].v = pos + rot * clipVertices[0].v;
clipVertices[1].v = pos + rot * clipVertices[1].v;
}