Ray-plane intersection to find the Z of the intersecting point

Question

I have a rectangle in 3d space (p1, p2, p3, p4) and when the mouse rolls over it I need to calculate the exact Z of the point on the rect, given the mouse coordinates (x, y).

Would a Ray-plane intersection find the Z of the intersecting point?

Edit: Would this one-liner work? .. it returns the t value for the intersection, apparently the Z value.

 float rayPlane(vector3D planepoint, vector3D normal, vector3D origin, vector3D direction){

     return -((origin-planepoint).dot(normal))/(direction.dot(normal));
 }

Well, it seems to be right. – Notabene Jan 12 '11 at 19:39 — Notabene, Jan 12 '11 at 19:39

Notabene · Accepted Answer · 2011-01-12T18:43:36.157

4

If you dont mind using your rect as two triangles, here is the code from my (working) raytracer:

//RAY-TRAINGLE test
Vec3f e1 = p2 - p1;
Vec3f e2 = p3 - p1;
Vec3f s1 = cross(aRay.dir, e2);

float divisor = dot(s1, e1);
if (divisor == 0.)
 return false; //not hit

float invDivisor = 1.f / divisor;

// Compute first barycentric coordinate
Vec3f d = aRay.org - p1;

float b1 = dot(d, s1) * invDivisor;
if (b1 < 0. || b1 > 1.)
 return false; // not hit

// Compute second barycentric coordinate
Vec3f s2 = cross(d, e1);
float b2 = dot(aRay.dir, s2) * invDivisor;
if (b2 < 0. || b1 + b2 > 1.)
 return false;

// Compute _t_ to intersection distance
float t = dot(e2, s2) * invDivisor; /// << HERE you go.
Vec3f intersection = aRay.org + t*aRay.dir;

edited Jan 12 '11 at 18:43

answered Jan 12 '11 at 18:33

Notabene

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@notabene - cross() and dot() are 3d matrix functions? or are they math for triangles? could I ask for those too :)? You see I'm porting it to a much dumber language... – Robin Rodricks Jan 12 '11 at 18:43
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@Jenko Yes float t is a Z value. And cross and dot are the algebraic functions. What language are you using. I'm sure that there is some kind of simple algebra library. – Notabene Jan 12 '11 at 18:51
@notabene - Thank you! I'll try it out and let you know if it works ... :) – Robin Rodricks Jan 12 '11 at 19:06
1

@Jenko - Yes you are always counting dot/cross product for 2 vectors. And good luck. – Notabene Jan 12 '11 at 19:13
@notabene - what does aRay.org and aRay.dir do? the origin and the direction of the vector? how can I calculate these? – Robin Rodricks Jan 12 '11 at 19:14
@Jenko - Correct: aRay.org is origin of the ray and aRay.dir is direction of the ray. – Notabene Jan 12 '11 at 19:15
@notabene - Nice. But what about divisor? what value is that? what can I keep it? I just need a simple ray to triangle intersection. – Robin Rodricks Jan 12 '11 at 19:19
@Jenko - Those IFs will tell you if triangle is actually hit. So you need it all. Divisor is scalar pointing float number (like 3.549). Result of dot product is one number. Result of cross product is new vector. – Notabene Jan 12 '11 at 19:23
@notabene - No, I like your code! very small and fast ... only problem is how to calculate the divisor? – Robin Rodricks Jan 12 '11 at 19:26
@Jenko - It seems that i should comment my code much more. I assumed that you know those stuff if you are making rays. BTW are you sure that rays are ok? – Notabene Jan 12 '11 at 19:27
It is the only way to calculate the intersection ... I want to calc the Z of a ray-rectangle intersection .. sorry for not understanding :) ... – Robin Rodricks Jan 12 '11 at 19:36
@Jenko - Your code in edit seems to be quite ok. Do you know how to compute normal? – Notabene Jan 12 '11 at 19:42
Yes. Don't forgot to normalize normal ;) – Notabene Jan 12 '11 at 19:44
Thank you very very much for all the help :) I will surely write back if it works ... thank you! – Robin Rodricks Jan 12 '11 at 19:51
You are welcome. But i am not sure if you did not solved it by yourself :-) – Notabene Jan 12 '11 at 19:52
@Jenko - Glad to hear it. – Notabene Jan 14 '11 at 07:37

Ray-plane intersection to find the Z of the intersecting point

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