public static bool Collide(out ContactManifold manifold,
CircleShape circle1, Transform2D transform1,
CircleShape circle2, Transform2D transform2)
{
var center1 = transform1.Transform(circle1.Center);
var center2 = transform2.Transform(circle2.Center);
// 两个圆是否碰撞，计算两个圆心的距离，是否比两者的半径之和小
var totalRadius = circle1.Radius + circle2.Radius;
if ((center1 - center2).LengthSquared() > totalRadius * totalRadius)
{
manifold = null;
return(false);
}
manifold = new ContactManifold()
{
LocalPoint = circle1.Center,
LocalNormal = Vector2D.Zero, // 为什么圆和圆的法线为 0 向量？
Points = new[] { new ContactPoint()
{
LocalPoint = circle2.Center
} },
};
return(true);
}
public static bool Collide(out ContactManifold manifold,
PolygonShape polygon1, Transform2D transform1,
PolygonShape polygon2, Transform2D transform2)
{
var radius = Configuration.PolygonRadius * 2;
var seperation1 = FindMaxSeperation(out int edge1, polygon1, transform1, polygon2, transform2);
if (seperation1 > radius)
{
manifold = null;
return(false);
}
var seperation2 = FindMaxSeperation(out int edge2, polygon2, transform2, polygon1, transform1);
if (seperation2 > radius)
{
manifold = null;
return(false);
}
var flip = 0;
var tol = 0.1f * Configuration.LinearSlop;
if (seperation2 > seperation1 + tol)
{
MathT.Swap(ref polygon1, ref polygon2);
MathT.Swap(ref transform1, ref transform2);
MathT.Swap(ref edge1, ref edge2);
flip = 1;
}
var incidentEdge = FindIncidentEdge(polygon1, transform1, edge1, polygon2, transform2);
throw new NotImplementedException();
}
public static bool Collide(out ContactManifold manifold,
PolygonShape polygon1, Transform2D transform1,
CircleShape circle2, Transform2D transform2)
{
// 将圆心坐标转换到多边形的本地坐标系中
var c = transform2.InverseTransform(transform1.Transform(circle2.Center));
var radius = Configuration.PolygonRadius + circle2.Radius;
var normalIndex = 0;
var seperation = float.MinValue;
for (int i = 0; i < polygon1.Verticles.Length; ++i)
{
// 将圆心到顶点的向量，投影到顶点所在边的法线上
var s = Vector2D.Dot(polygon1.Normals[i], c - polygon1.Verticles[i]);
// 如果投影长度大于圆的半径，即不存在相交
if (s > radius)
{
manifold = null;
return(false);
}
// 找到相交最浅的顶点
if (s > seperation)
{
normalIndex = i;
seperation = s;
}
}
// 得到最浅相交的接触边的两个顶点
var v1 = polygon1.Verticles[normalIndex];
var v2 = polygon1.Verticles[normalIndex + 1 < polygon1.Verticles.Length ? normalIndex + 1 : 0];
// 如果圆心在多边形内部
if (seperation < float.Epsilon)
{
manifold = new ContactManifold()
{
LocalPoint = (v1 + v2) * 0.5f,
LocalNormal = polygon1.Normals[normalIndex],
Points = new[] { new ContactPoint()
{
LocalPoint = circle2.Center
} }
};
return(true);
}
// 如果圆心的投影在 v1 顶点的外侧
var u1 = Vector2D.Dot(c - v1, v2 - v1);
if (u1 <= 0f)
{
if ((c - v1).LengthSquared() > radius * radius)
{
manifold = null;
return(false);
}
manifold = new ContactManifold()
{
LocalPoint = v1,
LocalNormal = c - v1,
Points = new[] { new ContactPoint()
{
LocalPoint = circle2.Center
} }
};
manifold.LocalNormal.Normalize();
return(true);
}
// 如果圆心的投影在 v2 顶点的外侧
var u2 = Vector2D.Dot(c - v2, v1 - v2);
if (u2 <= 0f)
{
if ((c - v2).LengthSquared() > radius * radius)
{
manifold = null;
return(false);
}
manifold = new ContactManifold()
{
LocalPoint = v2,
LocalNormal = c - v2,
Points = new[] { new ContactPoint()
{
LocalPoint = circle2.Center
} }
};
manifold.LocalNormal.Normalize();
return(true);
}
// 如果圆心的投影在 v1 和 v2 顶点的边上
{
var faceCenter = 0.5f * (v1 + v2);
var s = Vector2D.Dot(c - faceCenter, polygon1.Normals[normalIndex]);
if (s > radius)
{
manifold = null;
return(false);
}
manifold = new ContactManifold()
{
LocalPoint = faceCenter,
LocalNormal = polygon1.Normals[normalIndex],
Points = new[] { new ContactPoint()
{
LocalPoint = circle2.Center
} }
};
return(true);
}
}
