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POdraw 3d faces as 2d
 

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    <p>I have 3d mesh and I would like to draw each face a 2d shape.</p> <p>What I have in mind is this: for each face 1. access the face normal 2. get a rotation matrix from the normal vector 3. multiply each vertex to the rotation matrix to get the vertices in a '2d like ' plane 4. get 2 coordinates from the transformed vertices</p> <p>I don't know if this is the best way to do this, so any suggestion is welcome.</p> <p>At the moment I'm trying to get a rotation matrix from the normal vector, how would I do this ?</p> <p><strong>UPDATE:</strong></p> <p>Here is a visual explanation of what I need:</p> <p><img src="https://i984.photobucket.com/albums/ae330/orgicus/cube.gif" alt="3d to 2d"></p> <p>At the moment I have quads, but there's no problem converting them into triangles.</p> <p>I want to rotate the vertices of a face, so that one of the dimensions gets flattened. </p> <p>I also need to store the original 3d rotation of the face. I imagine that would be inverse rotation of the face normal.</p> <p>I think I'm a bit lost in space :)</p> <p>Here's a basic prototype I did using <a href="http://processing.org" rel="nofollow noreferrer">Processing</a>:</p> <pre><code>void setup(){ size(400,400,P3D); background(255); stroke(0,0,120); smooth(); fill(0,120,0); PVector x = new PVector(1,0,0); PVector y = new PVector(0,1,0); PVector z = new PVector(0,0,1); PVector n = new PVector(0.378521084785,0.925412774086,0.0180059205741);//normal PVector p0 = new PVector(0.372828125954,-0.178844243288,1.35241031647); PVector p1 = new PVector(-1.25476706028,0.505195975304,0.412718296051); PVector p2 = new PVector(-0.372828245163,0.178844287992,-1.35241031647); PVector p3 = new PVector(1.2547672987,-0.505196034908,-0.412717700005); PVector[] face = {p0,p1,p2,p3}; PVector[] face2d = new PVector[4]; PVector nr = PVector.add(n,new PVector());//clone normal float rx = degrees(acos(n.dot(x)));//angle between normal and x axis float ry = degrees(acos(n.dot(y)));//angle between normal and y axis float rz = degrees(acos(n.dot(z)));//angle between normal and z axis PMatrix3D r = new PMatrix3D(); //is this ok, or should I drop the builtin function, and add //the rotations manually r.rotateX(rx); r.rotateY(ry); r.rotateZ(rz); print("original: ");println(face); for(int i = 0 ; i &lt; 4; i++){ PVector rv = new PVector(); PVector rn = new PVector(); r.mult(face[i],rv); r.mult(nr,rn); face2d[i] = PVector.add(face[i],rv); } print("rotated: ");println(face2d); //draw float scale = 100.0; translate(width * .5,height * .5);//move to centre, Processing has 0,0 = Top,Lef beginShape(QUADS); for(int i = 0 ; i &lt; 4; i++){ vertex(face2d[i].x * scale,face2d[i].y * scale,face2d[i].z * scale); } endShape(); line(0,0,0,nr.x*scale,nr.y*scale,nr.z*scale); //what do I do with this ? float c = cos(0), s = sin(0); float x2 = n.x*n.x,y2 = n.y*n.y,z2 = n.z*n.z; PMatrix3D m = new PMatrix3D(x2+(1-x2)*c, n.x*n.y*(1-c)-n.z*s, n.x*n.z*(1-c)+n.y*s, 0, n.x*n.y*(1-c)+n.z*s,y2+(1-y2)*c,n.y*n.z*(1-c)-n.x*s,0, n.x*n.y*(1-c)-n.y*s,n.x*n.z*(1-c)+n.x*s,z2-(1-z2)*c,0, 0,0,0,1); } </code></pre> <p><strong>Update</strong></p> <p>Sorry if I'm getting annoying, but I don't seem to get it.</p> <p>Here's a bit of python using <a href="http://www.blender.org/documentation/249PythonDoc/Mathutils-module.html" rel="nofollow noreferrer">Blender</a>'s API:</p> <pre><code>import Blender from Blender import * import math from math import sin,cos,radians,degrees def getRotMatrix(n): c = cos(0) s = sin(0) x2 = n.x*n.x y2 = n.y*n.y z2 = n.z*n.z l1 = x2+(1-x2)*c, n.x*n.y*(1-c)+n.z*s, n.x*n.y*(1-c)-n.y*s l2 = n.x*n.y*(1-c)-n.z*s,y2+(1-y2)*c,n.x*n.z*(1-c)+n.x*s l3 = n.x*n.z*(1-c)+n.y*s,n.y*n.z*(1-c)-n.x*s,z2-(1-z2)*c m = Mathutils.Matrix(l1,l2,l3) return m scn = Scene.GetCurrent() ob = scn.objects.active.getData(mesh=True)#access mesh out = ob.name+'\n' #face0 f = ob.faces[0] n = f.v[0].no out += 'face: ' + str(f)+'\n' out += 'normal: ' + str(n)+'\n' m = getRotMatrix(n) m.invert() rvs = [] for v in range(0,len(f.v)): out += 'original vertex'+str(v)+': ' + str(f.v[v].co) + '\n' rvs.append(m*f.v[v].co) out += '\n' for v in range(0,len(rvs)): out += 'original vertex'+str(v)+': ' + str(rvs[v]) + '\n' f = open('out.txt','w') f.write(out) f.close </code></pre> <p>All I do is get the current object, access the first face, get the normal, get the vertices, calculate the rotation matrix, invert it, then multiply it by each vertex. Finally I write a simple output.</p> <p>Here's the output for a default plane for which I rotated all the vertices manually by 30 degrees:</p> <pre><code>Plane.008 face: [MFace (0 3 2 1) 0] normal: [0.000000, -0.499985, 0.866024](vector) original vertex0: [1.000000, 0.866025, 0.500000](vector) original vertex1: [-1.000000, 0.866026, 0.500000](vector) original vertex2: [-1.000000, -0.866025, -0.500000](vector) original vertex3: [1.000000, -0.866025, -0.500000](vector) rotated vertex0: [1.000000, 0.866025, 1.000011](vector) rotated vertex1: [-1.000000, 0.866026, 1.000012](vector) rotated vertex2: [-1.000000, -0.866025, -1.000012](vector) rotated vertex3: [1.000000, -0.866025, -1.000012](vector) </code></pre> <p>Here's the first face of the famous Suzanne mesh:</p> <pre><code>Suzanne.001 face: [MFace (46 0 2 44) 0] normal: [0.987976, -0.010102, 0.154088](vector) original vertex0: [0.468750, 0.242188, 0.757813](vector) original vertex1: [0.437500, 0.164063, 0.765625](vector) original vertex2: [0.500000, 0.093750, 0.687500](vector) original vertex3: [0.562500, 0.242188, 0.671875](vector) rotated vertex0: [0.468750, 0.242188, -0.795592](vector) rotated vertex1: [0.437500, 0.164063, -0.803794](vector) rotated vertex2: [0.500000, 0.093750, -0.721774](vector) rotated vertex3: [0.562500, 0.242188, -0.705370](vector) </code></pre> <p>The vertices from the Plane.008 mesh are altered, the ones from Suzanne.001's mesh aren't. Shouldn't they ? Should I expect to get zeroes on one axis ? Once I got the rotation matrix from the normal vector, what is the rotation on x,y,z ?</p> <p><em>Note:</em> 1. Blender's Matrix supports the * operator 2.In Blender's coordinate system Z point's up. It looks like a right handed system, rotated 90 degrees on X.</p> <p>Thanks</p>
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