Far clipping plane cuts at twice the declared distance

[zoncabe]

t3d_mat4_perspective mixes two depth conventions. Result: geometry stays
visible until twice the far plane passed to t3d_viewport_set_projection.

tiny3d/src/t3d/t3dmath.c

Line 153 in 73d822f

mat->m[2][2] = far / (near - far);

Cause

Constant term is written for the -1..1 depth convention, which carries a factor
of two:

m[3][2] = -2 * far * near / (far - near)

Z term is written for the 0..1 convention, which does not:

m[2][2] = far / (near - far)

Clip Z at eye distance d comes out as:

z = far/(far-near) * d - 2*far*near/(far-near)

Clipping tests z <= w, and w is d. Solving:

d * near/(far-near) <= 2*far*near/(far-near)
d <= 2*far

With the matching term -(far + near)/(far - near) the same solve gives
d <= far.

Near plane is unaffected: it solves to d >= near either way.

Measurement

Four posts on one axis, 10 metres apart, FPS camera walking the line, both
planes printed on screen. Far plane set to 25 metres, geometry disappears at
50.

Screenshots of both builds attached, before and after the fix. Both ROMs are
attached as well.

Fix

mat->m[2][2] = -(far + near) / (far - near);

Impact

Behaviour change, visible in every existing project. Scenes tuned against the
current behaviour lose whatever sat between the declared plane and its double.
Depth precision improves: that range currently compresses into the tail of the
depth buffer.

[HailToDodongo]

already fixed in PR #81