Ray To Plane Intersection
Posted 21 January 2007 - 04:55 AM
If I were doing this in C++ it wouldn't be too hard since, if you include the correct libraries, you can have datatypes like "Vector" which store <x,y,z> and do functions such as DotProduct. Unfortunately, since Game Maker only has "real" and "string" it is much harder. I looked up tutorials on Google and found some but they all assume that you can store variables as <x,y,z>.
I need some help with going about this in Game Maker. I've written a script to convert the plane coordinates to Ax+By+Cz+D = 0 format, and save A, B, C, and D so that they don't have to be re-calculated each time the plane is needed. I've also written a script to check whether a point lies on, behind, or in front of a plane. But I'm stuck on converting r(t) = p + tD (plane to ray check) to something Game Maker can use. Also, I need some help with a script for checking whether the point lies in a triangle.
Posted 21 January 2007 - 10:10 PM
For the point-in-triangle check, this should do the trick
Checks whether a point is inside a triangle
arguments0-1: coordinates of the point
arguments2-7: coordinates of the triangle
Returns true if so, false if not
return (abs(abs((argument2-argument0)*(argument5-argument1)-(argument4-argument0)*(argument3-argument1)) + abs((argument4-argument0)*(argument7-argument1)-(argument6-argument0)*(argument5-argument1)) + abs((argument6-argument0)*(argument3-argument1)-(argument2-argument0)*(argument7-argument1)) - abs((argument4-argument2)*(argument7-argument3)-(argument6-argument2)*(argument5-argument3))) <= 1 / 256);[/codebox]
Posted 21 January 2007 - 10:54 PM
You can "make" your own data types by grouping the native data structures. For example, you could have a ds_list, with index 0 being a ds_queue and 1 a stack, and so forth. It's tedious, but efficent (afaik)
I don't quite understand what that would do... and every time you used the "variable" you'd have to use ds_list functions, and also that still doesn't solve the problem of defining what operators do to different data types.
Anyways... I need to return the point of intersection as well. Does it seriously take that much code just to write out r(t) = p + tD just using reals?
EDIT: I forgot to mention I made a script for dot product, anything needing that can just be written Dot(vx1,vy1,vz1,vx2,vy2,vz2).
EDIT2: Ok, I've figured out how to do the ray-to-plane part, here it is:
// arg0-2 = point on plane // arg3-5 = plane normal // arg6-8 = origin of ray // arg9-11 = line vector px = argument0; py = argument1; pz = argument2; nx = argument3; ny = argument4; nz = argument5; ox = argument6; oy = argument7; oz = argument8; dx = argument9; dy = argument10; dz = argument11; /* t = -((<ox,oy,oz> - <px,py,pz>) . <nx,ny,nz>)/(<dx,dy,dz> . <nx,ny,nz>) <pntx,pnty,pntz> = <ox,oy,oz> + t*<dx,dy,dz> */ t = -(Dot(ox-px,oy-py,oz-pz,nx,ny,nz)/Dot(dx,dy,dz,nx,ny,nz)); pX = ox + t*dx; pY = oy + t*dy; pZ = oz + t*dz;
Now all I need is code to detect whether it actually hits the plane, because this gives coordinates no matter what, but I think I already have that. Now what I need is a script for whether the coordinates are in a triangle... or even better, the ray hits the triangle, because I can imagine that if I used coordinates, the script would always return false because of the limited accuracy on computers.
Edited by Gumgo, 22 January 2007 - 02:17 AM.
Posted 22 January 2007 - 11:09 AM
extentX = max(x1,x2,x3)-min(x1,x2,x3);
extentY = max(y1,y2,y3)-min(y1,y2,y3);
extentZ = max(z1,z2,z3)-min(z1,z2,z3);
The dimension you should ignore is indicated by whichever of extentX, extentY, extentZ is the smallest.
Edited by xot, 22 January 2007 - 11:38 AM.
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