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Ray Tracing - Weird edges of triangle.

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Hey, I just finished doing my ray-triangle intersection test. I made simple scene to test it. Just one triangle facing to the camera. I rendered it, and it works fine. I see the triangle. But at the bottom edge of the triangle, there are some weird artifacts. I'll post the code for intersection as well as the image of rendered image.

Image:
[spoiler]daJbW.png[/spoiler]

Code for intersection:
[spoiler]

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using OpenTK;

namespace RayTracing
{
public class Triangle : IIntersectable
{
public Vector3[] Verticies = new Vector3[3];
public Material Material { get; set; }

private const float Epilson = 1e-06f;

public Intersection Intersect(Ray ray)
{
Intersection its = new Intersection();
Vector3[] V = Verticies; // Just to save some time typing
its.Hit = false;

Vector3 diff = ray.Position - V[0];
Vector3 edge1 = V[1] - V[0];
Vector3 edge2 = V[2] - V[0];
Vector3 normal = Vector3.Cross(edge1, edge2);

float DdN = Vector3.Dot(ray.Direction, normal);
float sign;

if (DdN > Epilson)
{
sign = 1.0f;
}
else if (DdN < -Epilson)
{
sign = -1.0f;
DdN = -DdN;
}
else
{
//Ray is parallel to triangle. No intersection.
return its;
}

float DdQ = sign * Vector3.Dot(ray.Direction, Vector3.Cross(diff, edge2));

if (DdQ >= 0.0f)
{
float DdE = sign * Vector3.Dot(ray.Direction, Vector3.Cross(edge1, diff));

if (DdE >= 0.0f)
{
if (DdQ + DdE <= DdN)
{
float QdN = -sign * Vector3.Dot(diff, normal);

if (QdN >= 0.0f)
{
//float mTriBary1 = DdQ * inv;
//float mTriBary2 = DdE * inv;
//float mTriBary0 = 1.0f - mTriBary1 - mTriBary2;
float inv = 1.0f / DdN;
float t = QdN * inv;
its.Hit = true;
its.Material = this.Material;
its.Distance = t;
its.Position = Vector3.Multiply(ray.Direction, t);
its.Normal = normal;
}
}
}
}

return its;
}
}
}

[/spoiler]

Code for generating eye rays:
[spoiler]

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using OpenTK;

namespace RayTracing
{
public class Camera
{
public Vector3 Position { get; set; }
public Vector3 Rotation { get; set; }
public float FovX { get; set; }
public float FovY { get; set; }
public RayTracer RayTracer { get; set; }

private Matrix4 rotationMatrix = Matrix4.Identity;

public Camera(RayTracer r)
{
RayTracer = r;
FovX = MathHelper.PiOver4;
Update();

}

public Ray GetRay(int x, int y)
{
Ray r = new Ray();

float rX, rY;
rX = ((2.0f * (float)x - (float)RayTracer.Width) / (float)RayTracer.Width) * (float)Math.Tan(FovX);
rY = ((2.0f * (float)y - (float)RayTracer.Height) / (float)RayTracer.Height) * (float)Math.Tan(FovY);

r.Position = Position;
r.Direction = new Vector3(rX, rY, -1.0f);
r.Direction = Vector3.Normalize(r.Direction);
r.Direction = Vector3.Transform(r.Direction, rotationMatrix);

return r;
}

public void Update()
{
FovY = (float)RayTracer.Height / (float)RayTracer.Width * FovX;
rotationMatrix = Matrix4.CreateRotationX(Rotation.X) * Matrix4.CreateRotationY(Rotation.Y) * Matrix4.CreateRotationZ(Rotation.Z);
}


}
}

[/spoiler]

I think the problem is in generating eye rays, but I don't see anything wrong here.

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I don't really have an answer for you. It appears to me that all three edges are equally bad, but it's easier to tell on an axis aligned edge. Try it with a right angled triangle and that may show up more clearly.

Also try it with a simple plane test instead of a triangle, it may be easier to debug.

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You want to add epsilon comparisons when comparing DdQ, DdE, QdN, etc... as well, as they seem to relate to your intersection point's barycentric coordinates with respect to the triangle, so they will produce weird nondeterministic edges because of floating-point inaccuracies. At least that's all I can think of, and the image clearly reminds me of the same thing I had in my own raytracer (due to forgetting epsilons).

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Not exactly an answers, more like a guess but:

From a (very) quick look at the code, I assume you are taking a single sample per pixel. That will always generate edge artefacts. Try subdividing the pixel. You could start with a 2 by 2 and just average the results.

This is an assumption based on no data though ( can't see your raycast loop ) so take it as is.

P.S:
Bacterius makes a valid point too. I hit that block early as well. Wald's paper might help
This was also an eye opener when I was building my raytracer. Probably the most performance oriented intersection technique ( still using barycentric coords.) Edited by Tudor Nita

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yeah. 'edge' cases. Check your dividers multipliers. These usually produce artifacts when they get very small or very big, due to floating point innacuracies.

Or you can go 'double'. It' still not solving the problem.

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I think the problem is not inside that code snippet.
Is it maybe the case that you're normalizing your direction vector? in case you do, try it without normalization (shouldn't be important for this test, I guess).

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