plane formula, relative offset's to world space?

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2 comments, last by Sneftel 13 years, 9 months ago
hello, i'm trying to generate a plane shape by specifying the formula a+b+c+d=0, and a size value.

i.e: a standard 2D plane is: z+d=0(0x+0y+1z+d=0), now then, if i wanted to pull a square out of that plane, i'd simply specify 4 x/y values in the 4 quadrants, now then, this works fine and dandy in 2D because i know that the plane is facing forward, and only the x/y values can give me the shape i want from the plane, however what if the plane is say: .5y+.5z+d=0?, i want to still specify a 4 x/y points along the plane, but how would i translate those relative x/y points to world space?

sorry if this doesn't make much sense, i tried to explain it the best i could, and most of the material i found on the web has to do with distances and intercepts to a plane, but not how to specify points on the plane.

anywho, here's my current working code:

void CreatePlane(SPEVector4 Plane, float Size, SPEObject *Obj){	SPEVector4 P; memcpy(P, Plane, sizeof(SPEVector4));	Normalize(P);	SPEVertice *Verts = new SPEVertice[4];	Verts[0].x = (P[1]*Size+P[2]*Size);//+P[3];	Verts[0].y = (P[0]*Size+P[2]*Size);//+P[3];	Verts[0].z = (P[0]*Size+P[1]*Size);//+P[3];	Verts[1].x = (P[1]*Size+P[2]*Size);//+P[3];	Verts[1].y = (-P[0]*Size+P[2]*Size);//+P[3];	Verts[1].z = (-P[0]*Size+P[1]*Size);//+P[3];	Verts[2].x = (-P[1]*Size+P[2]*Size);//+P[3];	Verts[2].y = (-P[0]*Size+P[2]*Size);//+P[3];	Verts[2].z = (-P[0]*Size-P[1]*Size);//+P[3];	Verts[3].x = (-P[1]*Size+P[2]*Size);//+P[3];	Verts[3].y = (P[0]*Size+P[2]*Size);//+P[3];	Verts[3].z = (P[0]*Size-P[1]*Size);//+P[3];        ...	return;}

that doesn't work, i tried some things, but just couldn't figure it out, and i don't know the right words to google for something like this.
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Quote:hello, i'm trying to generate a plane shape by specifying the formula a+b+c+d=0, and a size value.
Hm, I'll take a guess at what you mean here. Do you mean you want to generate the vertices of a square or rectangle that lies in a specified plane, and has a specified position and dimensions?

The term 'plane shape' could probably use some clarification. I suppose a plane is a shape technically (an unbounded shape), but it's not something you can really directly represent graphically. Also, a+b+c+d=0 is not the equation of a plane; do you perhaps mean ax+by+cz+d=0?

If you could state more specifically what it is you're wanting to do, that would probably make it easier for us to help.
yes, you hit it right on the head, sorry about the formula being a bit off, i want to generate the point's of a square/rectangle that is found along a specified plane, basically if i want to find say an x of 10 along the plane, i want to know the world space of that relative x offset along the plane.
Check out https://www.facebook.com/LiquidGames for some great games made by me on the Playstation Mobile market.
To expand on what jyk said, you can specify a planar shape by its plane and some other information, but it's not a great way to do it. The beautiful thing about a plane, and the reason you can describe it just as Ax+By+Cz+D=0, is that it is invariant under tangent rotation and translation. That is, a plane which is parallel to the ground doesn't have any idea which way "north" is, and it doesn't know where your house is. Shift it over a few miles, turn it 45 degrees, and it's still the same plane. You need more tools of description if you want to talk about "where".

If you have a plane and want to make a figure on that plane, you need a basis, which is to say you need an origin and you need some axes. The plane normal will give you one axis, and you can use (-A*D, -B*D, -C*D) as your origin, but that still leaves you short a couple of axes. So the first thing you need is an outside, world-space vector that you know isn't normal to the plane; project it onto the plane and normalize it to get a tangent, use the cross product to get a third vector (the "bitangent"), and now you have your basis. This allows you to talk about "where" on the plane: Naming your origin point O, and your normal, tangent, and bitangent N, T, and B, a point on the plane expressed in plane coordinates u,v has world-space position O + uT + vB. Any such u,v will describe a point on the plane, and a shape described by u,v values which are "rectangular" in the normal sense of the word will be a rectangle in world-space.

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