What if we apply the transformation only on the vertices one by one? Right now we transform the triangle altogether, so have 4x4 * 4x3 => 4x3. If we do it by 4x4 * 4x1 three times for n1, n2 and n3, then the normal should still be correct right?
Max
Not quite sure what you mean - n1, n2, and n3 are the x, y, and z components of the normal vector. It would be correct to transform each vertex of the triangle and then re-compute the normal via the cross product, but that's not a possibility with other definitions of vertex normals.
Osoii
I'm a bit confused when watching the lecture about why setting homogeneous coordinate to zero can ignore the translation. Then I tried that matrix multiplication and found that changing that number to zero, will make u,v, and w becomes 0 in the addition. And the whole thing about raising up dimension really broaden my mind.
dnialh
Does it make sense to think about this as vectors being the difference between two points in space, so the 1s in the 4th co-ordinate cancelling out? I was thinking about it like this, but the I realized that it doesn't fully make sense, as it only works if we 'subtract' two points with the same 4th coordinate (and the scaling of the vector depends on what exactly the 4th coordinate was).
What if we apply the transformation only on the vertices one by one? Right now we transform the triangle altogether, so have 4x4 * 4x3 => 4x3. If we do it by 4x4 * 4x1 three times for n1, n2 and n3, then the normal should still be correct right?
Not quite sure what you mean - n1, n2, and n3 are the x, y, and z components of the normal vector. It would be correct to transform each vertex of the triangle and then re-compute the normal via the cross product, but that's not a possibility with other definitions of vertex normals.
I'm a bit confused when watching the lecture about why setting homogeneous coordinate to zero can ignore the translation. Then I tried that matrix multiplication and found that changing that number to zero, will make u,v, and w becomes 0 in the addition. And the whole thing about raising up dimension really broaden my mind.
Does it make sense to think about this as vectors being the difference between two points in space, so the 1s in the 4th co-ordinate cancelling out? I was thinking about it like this, but the I realized that it doesn't fully make sense, as it only works if we 'subtract' two points with the same 4th coordinate (and the scaling of the vector depends on what exactly the 4th coordinate was).