Vec3 * Mat4x4

Newbie & Debugging Questions
#1

I am a newbie at matrices.
So my question is simple, how would I go about doing the following multiplication ?

Vec3 * Mat4x4

#2

Very carefully…


public void transform(Matrix4x4 m, Vec3 in, Vec3i out) {
  out.x = (in.x * m.e00) + (in.y * m.e01) + (in.z * m.e02) + m.e03;
  out.y = (in.x * m.e10) + (in.y * m.e11) + (in.z * m.e12) + m.e13;
  out.z = (in.x * m.e20) + (in.y * m.e21) + (in.z * m.e22) + m.e23;
}
#3

Thanks a lot, that finally finished my skinning process!

I really need to take some time to sit down and learn more of them matrices.

#4

My opinion here is that you’d be better off understanding vectors and coordinate frames first. Linear algebra is ‘just’ folding a couple of operations into a logically single one for affine transforms.

#5

“coordinate frames” ? :slight_smile:

#6

The linear algebra course on Khan Academy is pretty good.

#7

Just to elaborate on ClickerMonkey’s perfectly correct answer:

You can’t generally multiply a vector of 3 components with a 4x4 matrix, but the standard geometric interpretation of a 4x4 matrix is of an affine transform in homogeneous coordinate space. A vector in 3d Cartesian space (x,y,z) is a vector in homogeneous space (x,y,z,w) where w=1. So long story short, you turn your vec3(x,y,z) into a vec4(x,y,z,1) and then do normal matrix multiplication with it.

#8

Agreed! Transforming vectors need a w value of 0 and transforming points need a value of 1!

w is this neat part of a vector, if you set it to the square root of a point, the point is interpreted by OpenGL or a Matrix as a normalized vector.


v.w = (float)Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z);

Point/Vector is now normalized!

Full transform method with Vec4


out.x = (in.x * e00) + (in.y * e01) + (in.z * e02) + (in.w * e03);
out.y = (in.x * e10) + (in.y * e11) + (in.z * e12) + (in.w * e13);
out.z = (in.x * e20) + (in.y * e21) + (in.z * e22) + (in.w * e23);
out.w = (in.x * e30) + (in.y * e31) + (in.z * e32) + (in.w * e33);