Ray tracing ray-disk intersection

0
votes

So I'm trying to write code that sees if a ray intersects a flat circular disk and I was hoping to get it checked out here. My disk is always centered on the negative z axis so its normal vector should be (0,0, -1).

The way I'm doing it is first calculate the ray-plane intersection and then determining if that intersection point is within the "scope" of the disk.

In my code I am getting some numbers that seem off and I am not sure if the problem is in this method or if it is possibly somewhere else. So if there is something wrong with this code I would appreciate your feedback! =)

Here is my code: 

float d = z_intercept; //This is where disk intersects z-axis. Can be + or -.
ray->d = Normalize(ray->d); 
Point p(0, 0, d); //This is the center point of the disk
Point p0(0, 1, d);
Point p1(1, 0, d);
Vector n = Normalize(Cross(p0-p, p1-p));//Calculate normal

float diameter = DISK_DIAMETER; //Constant value
float t = (-d-Dot(p-ray->o, n))/Dot(ray->d, n); //Calculate the plane intersection
Point intersection = ray->o + t*ray->d;
return (Distance(p, intersection) <= diameter/2.0f); //See if within disk


//This is my code to calculate distance
float RealisticCamera::Distance(Point p, Point i) 
{
return sqrt((p.x-i.x)*(p.x-i.x) + (p.y-i.y)*(p.y-i.y) + (p.z-i.z)*(p.z-i.z));
}
2
mathgraphicsgeometryintersectionraytracing
Have you tested it? Does it work? What is your question? - Beta
My question is is this the proper way to go about calculating the intersection. I'm getting some numbers that are off and I am not sure if the bug is located in this part of my code or if it is possibly located elsewhere. So if I can get feedback that this is correct or incorrect, then it'll help me debug. - user1782677
You're getting some numbers that are off; You should have said so in the first place. It would be very helpful if you would now give us enough information to reproduce the bug (i.e. a minimal complete example) or at least the details of a case in which the results are off (i.e. the numbers you put in, the numbers you get out, the numbers you get along the way, and which of those seem off and why). - Beta
A little research on the net could have taken you a long way;-) scratchapixel.com/lessons/3d-basic-lessons/… - user18490

2 Answers

1
votes

"My disk is always centered on the negative z axis so its normal vector should be (0,0, -1)."

This fact simplifies calculations.

Degenerated case: ray->d.z = 0 -> if ray->o.z = d then ray lies in disk plane, check as 2Dd, else ray is parallel and there is no intersection

Common case: t = (d - ray->o.z) / ray->d.z

If t has positive value, find x and y for this t, and check x^2+y^2 <= disk_radius^2

0
votes

Calculation of t is wrong.

Points on the ray are:

ray->o + t * ray->d

in particular, coordinate z of a point on the ray is:

ray->o.z() + t * ray->d.z()

Which must be equal to d. That comes out

t = ( d - ray->o.z() ) / ray->d.z()