Quote:Yes, the caller can pass the actual corner coordinates of the roof - in addition to the normal and the center point. I think that should take care of the roof orientation. This roof-plane would be my construction plane on which my code would be performing operations to layout tiles, etc. I believe the main problem, in general, is how to transform points from one coordinate space to another - and defining appropriate transformation definition for that - this is what I remember from my high school math - but don't know how to do that. Is there a way to attach graphics to the messages in this forum?

Quote:Original post by jyk
Do you know that all roof surfaces will have four corners and be rectangular? Also, do you know what order the corners will be in? (E.g. in order clockwise, in order counterclockwise, etc.)

Quote:Square roof is a simple case - later there might be roofs with more complex shapes. Would it be easy if the caller provides the origin, x-axis, y-axis, and the actual roof boundary coordinates in 3d? Meanwhile, I will try and create the image to convey graphically.

Quote:Original post by jyk
Do you know what order the boundary vertices will be in? Will they be in CW or CCW order? Will they always form a convex polygon, or could they form a simple (possibly non-convex) polygon?

Quote:Original post by jyk
Hm, I guess I'm not entirely clear on what part you need help with. What you've described is a simple coordinate transform. You create (for example) a 4x4 matrix representing the roof surface's world transform, and then use that matrix to transform geometry from local space to world space as needed.

What math library are you using for this?

Quote:My main problem is with defining this world transform matrix - how to define it given the roof geometry, etc.

vector3 edge1 = vert[1] - vert[0];vector3 edge2 = vert[2] - vert[1];// If the normal ends up pointing the wrong way, reverse the order// of the arguments here:vector3 z = unit_cross(edge1, edge2);vector3 x = normalize(edge1);vector3 y = cross(z, x);vector3 origin = vert[0];// Now load x, y, z, and 'origin' into a 4x4 matrix.

Quote:I am not using any specific math library - I have used the vector and matrix routines that I have required so far from the articles in the gamedev.net. Do you recommend any specific library for this purpose?

Quote:Original post by jyk
Assuming the input polygon doesn't have any collinear or nearly collinear edges, you can compute the normal by taking the (normalized) cross product of any two consecutive edges.

Once you have the normal, you can compute the next basis vector by normalizing the first edge of the polygon (this is arbitrary, but it seems like a reasonable choice). Once you have two basis vectors, the third can be computed as the cross product of the first two. For the origin of the coordinate system, you can use the first vertex of the polygon.

Once you have the three basis vectors and the position vector, you can load them directly into the rows or columns of a 4x4 matrix (rows for row vectors, columns for column vectors).
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Quote:A good math library will make this a lot easier. What language are you programming in? (I can't remember if you've already mentioned this...)