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Editorial Team
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Asked: 2026-05-27T21:19:20+00:00

Alright, so I’m working on a ray tracer using phong shading. So far, everything

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Alright, so I’m working on a ray tracer using phong shading. So far, everything is good. I’ve cast rays that have hit the spheres in my scene, applied phong shading to them, and it looks normal.

Now, I’m calculating shadow rays, which is shooting a ray from the point of intersection from the primary ray to the light source, and seeing if it hits any objects on the way. If it does, then it’s in a shadow.

However, when computing whether the shadow ray hits any spheres, there seems to be an error with my discriminant that is calculated, which is odd since it’s been correct so far for primary rays.

Here’s the setup:

// Origin of ray (x,y,z)
origin: -1.9865333, 1.0925934, -9.8653316
// Direction of ray (x,y,z), already normalized
ray: -0.99069530, -0.13507602, -0.016648887

// Center of sphere (x,y,z)
cCenter: 1.0, 1.0, -10.0
// Radius of the sphere (x,y,z)
cRadius: 1.0

, and here’s the code for finding the discriminant:

// A = d DOT d
float a = dotProd(ray, ray);

// B = 2 * (o - c) DOT d
Point temp (2.0*(origin.getX() - cCenter.getX()), 2.0*(origin.getY() - cCenter.getY()), 2.0*(origin.getZ() - cCenter.getZ()));
float b = dotProd(temp, ray);

// C = (o - c) DOT (o - c) - r^2
temp.setAll(origin.getX() - cCenter.getX(), origin.getY() - cCenter.getY(), origin.getZ() - cCenter.getZ());
float c = dotProd(temp, temp);
c -= (cRadius * cRadius);

// Find the discriminant (B^2 - 4AC)
float discrim = (b*b) - 4*a*c;

Clearly, the ray is pointing away from the sphere, yet the discriminant here is positive (2.88) indicating that the ray is hitting the sphere. And this code works fine for primary rays as their discriminants must be correct, yet not for these secondary shadow rays.

Am I missing something here?

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1 Answer

  1. Editorial Team

    So short answer for my problem, in case someone finds this and has the same problem:

    The discriminant tells you whether a hit exists for a line (and not for a ray, like I thought). If it’s positive, then it has detected a hit somewhere on the line.

    So, when calculating the t-value(s) for the ray, check to see if they’re negative. If they are, then it’s a hit BEHIND the point of origin of the ray (ie. the opposite direction of the ray), so discard it. Only keep the positive values, as they’re hits in the direction of the ray.

    Even shorter answer: discard negative t-values.

    Credit goes to woodchips for making me realize this.

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