I have coordinates for 4 vertices/points that define a plane and the normal/perpendicular. The plane has an arbitrary rotation applied to it.
How can I 'un-rotate'/translate the points so that the plane has rotation 0 on x,y,z ?
I've tried to get the plane rotation from the plane's normal:
rotationX = atan2(normal.z,normal.y); rotationY = atan2(normal.z,normal.x); rotationZ = atan2(normal.y,normal.x);
Is this correct ?
How do I apply the inverse rotation to the position vectors ?
I've tried to create a matrix with those rotations and multiply it with the vertices, but it doesn't look right.
At the moment, I've wrote a simple test using Processing and can be seen here:
float s = 50.0f;//scale/unit PVector[] face = {new PVector(1.08335042,0.351914703846,0.839020013809), new PVector(-0.886264681816,0.69921118021,0.839020371437), new PVector(-1.05991327763,-0.285596489906,-0.893030643463), new PVector(0.909702301025,-0.63289296627,-0.893030762672)}; PVector n = new PVector(0.150384, -0.500000, 0.852869); PVector[] clone; void setup(){ size(400,400,P3D); smooth(); clone = unRotate(face,n,true); } void draw(){ background(255); translate(width*.5,height*.5); if(mousePressed){ rotateX(map(mouseY,0,height,0,TWO_PI)); rotateY(map(mouseX,0,width,0,TWO_PI)); } stroke(128,0,0); beginShape(QUADS); for(int i = 0 ; i < 4; i++) vertex(face[i].x*s,face[i].y*s,face[i].z*s); endShape(); stroke(0,128,0); beginShape(QUADS); for(int i = 0 ; i < 4; i++) vertex(clone[i].x*s,clone[i].y*s,clone[i].z*s); endShape(); } //get rotation from normal PVector getRot(PVector loc,Boolean asRadians){ loc.normalize(); float rz = asRadians ? atan2(loc.y,loc.x) : degrees(atan2(loc.y,loc.x)); float ry = asRadians ? atan2(loc.z,loc.x) : degrees(atan2(loc.z,loc.x)); float rx = asRadians ? atan2(loc.z,loc.y) : degrees(atan2(loc.z,loc.y)); return new PVector(rx,ry,rz); } //translate vertices PVector[] unRotate(PVector[] verts,PVector no,Boolean doClone){ int vl = verts.length; PVector[] clone; if(doClone) { clone = new PVector[vl]; for(int i = 0; i
Any syntax/pseudo code or explanation is useful.
What trying to achieve is this: If I have a rotated plane:
How can move the vertices to have something that would have no rotation:
Thanks!
UPDATE:
@muad
I'm not sure I understand. I thought I was using matrices for rotations. PMatrix3D's rotateX,rotateY,rotateZ calls should done the rotations for me. Doing it manually would be declaring 3d matrices and multiplying them. Here's a little snippet to illustrate this:
PMatrix3D rx = new PMatrix3D(1, 0, 0, 0, 0, cos(rot.x),-sin(rot.x), 0, 0, sin(rot.x),cos(rot.x) , 0, 0, 0, 0, 1); PMatrix3D ry = new PMatrix3D(cos(rot.y), 0,sin(rot.y), 0, 0, 1,0 , 0, -sin(rot.y), 0,cos(rot.y), 0, 0, 0,0 , 1); PMatrix3D rz = new PMatrix3D(cos(rot.z),-sin(rot.z), 0, 0, sin(rot.z), cos(rot.z), 0, 0, 0 , 0, 1, 0, 0 , 0, 0, 1); PMatrix3D r = new PMatrix3D(); r.apply(rx);r.apply(ry);r.apply(rz); //test PMatrix rmat = new PMatrix3D();rmat.rotateX(rot.x);rmat.rotateY(rot.y);rmat.rotateZ(rot.z); float[] frmat = new float[16];rmat.get(frmat); float[] fr = new float[16];r.get(fr); println(frmat);println(fr); /* Outputs: [0] 0.059300933 [1] 0.09312407 [2] -0.99388695 [3] 0.0 [4] 0.90466285 [5] 0.41586864 [6] 0.09294289 [7] 0.0 [8] 0.42198166 [9] -0.9046442 [10] -0.059584484 [11] 0.0 [12] 0.0 [13] 0.0 [14] 0.0 [15] 1.0 [0] 0.059300933 [1] 0.09312407 [2] -0.99388695 [3] 0.0 [4] 0.90466285 [5] 0.41586864 [6] 0.09294289 [7] 0.0 [8] 0.42198166 [9] -0.9046442 [10] -0.059584484 [11] 0.0 [12] 0.0 [13] 0.0 [14] 0.0 [15] 1.0 */