求解齐次坐标 (x,y,z,w) 中两个 3D 向量的叉积

Question

I want to calculate the cross product of x and vector y without numpy or any imports.

x = Vector(1,2,1,0)  
y = Vector(0,1,2,1)

but my result is always wrong. what am i missing here?

def crossproduct(x, y):
        final = Vector()
        final.v[0] = y.v[1] * v.v[2] - x.v[2] * y.v[1]
        final.v[1] = y.v[2] * v.v[3] - x.v[3] * y.v[2]
        final.v[2] = y.v[3] * v.v[0] - x.v[0] * y.v[3] 
        final.v[3] = y.v[0] * v.v[1] - x.v[1] * y.v[0]
        return final

Answer 1

Solving cross on a Vec4 (homogenuous) is the same as solving it as a Vec3 (Cartesian), since you're in 3 dimensions, no matter how you use the w component.

Check your cross formula, the one I usually use looks like this:

crossX = vector1.Y * vector2.Z - vector2.Y * vector1.Z
crossY = -(vector1.X * vector2.Z - vector2.X * vector1.Z)
crossZ = vector1.X * vector2.Y - vector2.X * vector1.Y
crossW = 0.0