Comment by vlasev

Woah this is really cool and an awesome point of view. Collapsing along the x-axis is just a projection along the vector [1, 0, 0] onto the the y-z plane defined by it and the origin. Then if you project along the vector [1, 1, 0] onto the plane defined by [1, -1, 0] and [0, 0, 1], you get the convolution.