get_sphere_uv does not correspond to its explanation #533
Description
The function get_sphere_uv in NextWeek listing 42 at section Texture 6.1, is given as
void get_sphere_uv(const point3& p, double& u, double& v) {
auto phi = atan2(p.z(), p.x());
auto theta = asin(p.y());
u = 1-(phi + pi) / (2*pi);
v = (theta + pi/2) / pi;
}whereas in the formula given in the explanation is:
To compute θ and ϕ, for a given hitpoint, the formula for
spherical coordinates of a unit radius sphere on the origin is:
x=cos(ϕ)cos(θ)
y=sin(ϕ)cos(θ)
z=sin(θ)
We need to invert that. Because of the lovely <cmath>
function atan2() (which takes any number proportional
to sine and cosine and returns the angle), we can pass in x
and y (the cos(θ) cancel):
ϕ=atan2(y,x)
The atan2
returns values in the range −π to π, so we need to
take a little care there. The θ is more straightforward:
θ=asin(z)
which returns numbers in the range −π/2
to π/2.
The problem also exist in dev-major branch.