平面实体上的立方体实体碰撞

Question

我怎么做一个立方体和一个平面之间的碰撞，我可以在平面上做一个球体，但我不能在平面上计算出立方体，我知道我必须找到这个立方体的x，y，z，然后在平面上做一个检测，但是我做不出来。

这是我的碰撞测试器代码。

public static bool sphereAndSphere(Sphere a, Sphere b, ref Contact contact)
    {
        // Get the vector from the centre of particle B to the centre of particle A
        Vector3 separationVector = b.Position - a.Position;
        float sumOfRadii = a.Radius + b.Radius;
        float distance = separationVector.Length();

        if (distance < sumOfRadii)
        {
            contact.contactPoint = a.Position + separationVector / 2f;
            separationVector.Normalize();
            contact.contactNormal = separationVector;
            contact.penetrationDepth = sumOfRadii - distance;

            return true;
        }

        return false;
    }

    // This assumes that the Origin is in the centre of world 
    // and that the planes are the boundaries of the world and that all rigid-bodies are within the boundaries
    public static bool sphereAndPlane(Sphere a, PlaneEntity b, ref Contact contact)
    {
        // Depth of sphere into plane (if negative, no collision)
        float depth = Vector3.Dot(a.Position, b.DirectionFromOrigin) + a.Radius + b.OffsetFromOrigin;

        if (depth > 0)
        {
            contact.contactPoint = a.Position + (a.Radius - depth) * b.DirectionFromOrigin;
            contact.contactNormal = -b.DirectionFromOrigin;
            contact.penetrationDepth = depth;

            return true;
        }

        return false;
    }

这是一个关于魔方的测试

public static bool sphereAndBox(Sphere a, Cube b, ref Contact contact)
    {
        Vector3 relativePoint = Vector3.Transform(a.Position, Matrix.Invert(b.WorldTransform));

        // Early out check, based on separation axis theorem
        if (Math.Abs(relativePoint.X) - a.Radius > b.halfSize.X
            || Math.Abs(relativePoint.Y) - a.Radius > b.halfSize.Y
            || Math.Abs(relativePoint.Z) - a.Radius > b.halfSize.Z)
            return false;

        Vector3 closestPoint = Vector3.Zero;

        closestPoint.X = MathHelper.Clamp(relativePoint.X, -b.halfSize.X, b.halfSize.X);
        closestPoint.Y = MathHelper.Clamp(relativePoint.Y, -b.halfSize.Y, b.halfSize.Z);
        closestPoint.Z = MathHelper.Clamp(relativePoint.Z, -b.halfSize.Z, b.halfSize.Z);

        float distance = (closestPoint - relativePoint).LengthSquared();

        if (distance < a.Radius * a.Radius)
        {
            contact.contactPoint = Vector3.Transform(closestPoint, b.WorldTransform);
            contact.contactNormal = a.Position - contact.contactPoint;
            contact.contactNormal.Normalize();
            contact.penetrationDepth = a.Radius - (float)Math.Sqrt(distance);
            return true;
        }

        return false;
}

Answer 1

如果平面或立方体没有轴对齐，或者立方体(宽度、长度、高度)不相等，您会发现针对平面单独测试立方体的每个角位置最容易，而不是将立方体作为一个整体进行测试。然后，当第一个角点穿过平面时，注册碰撞。

但是，如果平面和立方体都是轴对齐的，并且立方体是对称的(WLH)，那么可以将立方体视为半径为立方体宽度一半的球体。