/*
* 矩形，圆形的相交测试。
* 转到矩形的局部坐标系
* 然后把相对位置移动到第一象限
* 求出圆心到矩形的最近的点。
*/
public static bool DetectSquareCircle(SquareCollider bodyA, CircleCollider bodyB)
{
Vector2 hA = 0.5f * bodyA.width;
Vector2 hB = new Vector2(bodyB.radius, bodyB.radius);
Vector2 posA = bodyA.position;
Vector2 posB = bodyB.position;
Mat22 RotA = new Mat22(bodyA.rotation);
Mat22 RotAT = RotA.Transpose();
Vector2 dp = posB - posA; // 距离向量
Vector2 dA = RotAT * dp; // 距离向量，在A的局部坐标系里面表现
Vector2 v = MathUtils.Abs(dA); // 转到第一象限
Vector2 u = MathUtils.Max(v - hA, 0); // 求出最近的点（因为在第一象限，而且是在矩形的坐标系里面，所以可以这么写）
return(u.sqrMagnitude <= bodyB.radius * bodyB.radius); // 计算距离
}
/* 矩形相交测试。
* 使用Separating Axis Theorem，
* A，B矩形，
* 先转到A的坐标系中，然后对比他们的AABB，如果有一个不相交，那么就没碰撞。
* 同理B
*/
public static bool DetectTwoSquare(SquareCollider bodyA, SquareCollider bodyB)
{
Vector2 hA = 0.5f * bodyA.width;
Vector2 hB = 0.5f * bodyB.width;
Vector2 posA = bodyA.position;
Vector2 posB = bodyB.position;
Mat22 RotA = new Mat22(bodyA.rotation);
Mat22 RotB = new Mat22(bodyB.rotation);
Mat22 RotAT = RotA.Transpose(); // Transpose=>相反的转向
Mat22 RotBT = RotB.Transpose();
Vector2 dp = posB - posA; // 距离向量
Vector2 dA = RotAT * dp; // 距离向量，在A的局部坐标系里面表现
Vector2 dB = RotBT * dp; // 距离向量，在B的局部坐标里面的表现。
Mat22 C = RotAT * RotB; // B转到A的坐标系的旋转矩阵
Mat22 absC = MathUtils.Abs(C); // absC跟向量相乘，可以向量的aabb。
Mat22 absCT = absC.Transpose(); // 反着转
// Box A faces
// MathUtils.Abs(dA) 是把向量弄到第一象限，hA本来就是第一象限，absC*hB = 可以得到矩形的aabb
Vector2 faceA = MathUtils.Abs(dA) - hA - absC * hB;
if (faceA.x > 0.0f || faceA.y > 0.0f)
{
return(false);
}
// Box B faces
Vector2 faceB = MathUtils.Abs(dB) - absCT * hA - hB;
if (faceB.x > 0.0f || faceB.y > 0.0f)
{
return(false);
}
return(true);
}
// 切换到矩形的local坐标系
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
public static bool RaycastSquare(SquareCollider body, RayCollider line, out Vector2 normal, out float fraction)
{
normal = Vector2.zero;
fraction = 0;
Mat22 RotA = new Mat22(body.rotation);
Mat22 RotAT = RotA.Transpose();
Vector2 p1 = RotAT * (line.p1 - body.position) + body.position;
Vector2 p2 = RotAT * (line.p2 - body.position) + body.position;
Vector2 d = p2 - p1;
float lower = 0.0f, upper = 1;
int index = -1;
for (int i = 0; i < 4; ++i)
{
Vector2 v = body.position + SquareCollider.vecties[i] * body.width;
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
float numerator = Vector2.Dot(SquareCollider.normals[i], v - p1);
float denominator = Vector2.Dot(SquareCollider.normals[i], d);
if (denominator == 0.0f)
{
if (numerator < 0.0f)
{
return(false);
}
}
else
{
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower > numerator.
if (denominator < 0.0f && numerator < lower * denominator)
{
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
}
else if (denominator > 0.0f && numerator < upper * denominator)
{
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
// The use of epsilon here causes the assert on lower to trip
// in some cases. Apparently the use of epsilon was to make edge
// shapes work, but now those are handled separately.
//if (upper < lower - b2_epsilon)
if (upper < lower)
{
return(false);
}
}
Assert.IsTrue(0.0f <= lower && lower <= 1);
if (index >= 0)
{
fraction = lower;
normal = RotA * SquareCollider.normals[index];
return(true);
}
return(false);
}