Jacobian of projectCenterPx with respect to the view-space point: the 2×3
matrix that maps a splat's view-space covariance to its screen covariance.
Returned as three columns (one per view-space axis), each a screen vector,
matching the shader's mat3x2 J / J[0..2] layout.
General form, valid for any projection: with clip = P·(c, 1) and w = clip.w,
J[i][k] = ½·res_i·(P[i][k]/w − clip_i·P[3][k]/w²). For the symmetric
perspective P three builds this reduces to the historical
[[fx/z, 0], [0, fy/z], [fx·x/z², fy·y/z²]], and for an orthographic P
(w = 1, P[3][k] = 0) to [[fx, 0], [0, fy], [0, 0]].
Jacobian of
projectCenterPxwith respect to the view-space point: the 2×3 matrix that maps a splat's view-space covariance to its screen covariance. Returned as three columns (one per view-space axis), each a screen vector, matching the shader'smat3x2 J/J[0..2]layout.General form, valid for any projection: with clip = P·(c, 1) and w = clip.w,
J[i][k] = ½·res_i·(P[i][k]/w − clip_i·P[3][k]/w²). For the symmetric perspective P three builds this reduces to the historical[[fx/z, 0], [0, fy/z], [fx·x/z², fy·y/z²]], and for an orthographic P (w = 1, P[3][k] = 0) to[[fx, 0], [0, fy], [0, 0]].