Need clarification for computing normal of a sphere
Posted on 2008-11-01
I am trying to compute the 3D surface normal for a given point on a sphere, in order to find the direction of a light source. I am given the sphere's orthographic projection on the image plane, which is basically a circle, and I have found the center, radius, and area of this circle.
Given that the equation of a sphere is (x-xc)^2 + (y-yc)^2 + (z-zc)^2 = r^2, where xc,yc, and zc are the coordinates of the centroid of the sphere. I have solved for (z-zc) using this equation. I just want to make sure: if I compute the gradient (2(x-xc), 2(y-yc), 2(z-zc)), it safe to assume that the sphere's gradient will give me the normal vector TO the sphere's surface at the point (x,yz)? (the normal originates at the sphere's center)