meaning of m34 of CATransform3D

Question

What's the meaning of m34 of the structure CATransform3D, I only know it can change the perspective, but what's the meaning when the value is -0.001 and 0.001?

Answer 1

You can find the full details here. Note that Apple uses the reversed multiplication order for projection (relative to the given link) so all matrix multiplications are reversed and all matrices are transposed.

A short description of the meaning:

• m34 = 1/z distance to projection plane (the 1/e_z term in the reference link)
• + for the z axis is towards the viewer, resulting in a "looking in the mirror" feel when using -
• projection center is (0,0,0) plus any translations you set up

Answer 2

I read some articles including this one: https://developer.apple.com/library/content/documentation/Cocoa/Conceptual/CoreAnimation_guide/AdvancedAnimationTricks/AdvancedAnimationTricks.html#//apple_ref/doc/uid/TP40004514-CH8-SW13

My solutions is here:

Entities:

• eye - distance from screen to eye
• scale - visual scale of transformed object
• distance - distance to transformed object

Connecting formulas:

• scale = eye / (eye + distance)
• distance = eye * (1.0/scale - scale)
• eye = distance / (1.0/scale - scale)

Example of computing z-distance for desized scale of selected eye distance:

CATransform3D transformByScaleAndEye(CGFloat scale, CGFloat eye) {
    CATransform3D t = CATransform3DIdentity;
    t.m34 = -1.0 / eye;
    CGFloat distance = -eye*(1.0/scale - scale);
    return CATransform3DTranslate(t, 0, 0, distance);
}