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Draw 3d faces as 2d

I have a 3d mesh and I would like to draw every face of the 2nd shape.

What I mean: for each face 1. Access to the face is normal 2. get the rotation matrix from the normal vector 3. multiply each vertex by the rotation matrix to get the vertices in the "2d like" plane 4. get 2 coordinates from the converted vertices

I do not know if this is the best way to do this, so any suggestion is welcome.

I'm currently trying to get the rotation matrix from a normal vector, how would I do it?

UPDATE:

Here is a visual explanation of what I need:

3d to 2d

At the moment I have ATVs, but there is no problem turning them into triangles.

I want to rotate the tops of the face, so that one of the sizes is smoothed.

I also need to keep the original 3D face rotation. I assume that it will be normal reverse rotation of the face.

I think I lost a little in space :)

Here is the basic prototype I used with Processing :

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 < 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 < 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);
}

Update

Sorry if I annoy, but I don't seem to understand.

Here's some python using the Blender API:

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

All I do is get the current object, access the first person, get the normal value, get the vertices, calculate the rotation matrix, invert it, and then multiply by each vertex. Finally, I am writing a simple conclusion.

Here is the output for the default plane, for which I rotated all the vertices manually by 30 degrees:

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)

Here is the first face of Suzanne's famous net:

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)

Plane.008 , - Suzanne.001 mesh . ? ? , x, y, z?

: 1. Blender * 2. Z . , 90 X.

+3
4

. , . . 0. , .

? , . , . A,B,C. , A B. x AB. A 0,0. B 0,|AB|. C , AC AB ( ) |AC|.

+2

m. , . "" . face2d x, x. , 2d- . ( , .)

, (), , m.invert() . , - . , , , .

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];

  //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_inverse = 
      new PMatrix3D(x2+(1-x2)*c, n.x*n.y*(1-c)+n.z*s, n.x*n.y*(1-c)-n.y*s, 0,
                    n.x*n.y*(1-c)-n.z*s,y2+(1-y2)*c,n.x*n.z*(1-c)+n.x*s,   0,
                     n.x*n.z*(1-c)+n.y*s,n.y*n.z*(1-c)-n.x*s,z2-(1-z2)*c,  0,
                    0,0,0,1);

  face2d[0] = m_inverse * p0; // Assuming there an appropriate operator*().
  face2d[1] = m_inverse * p1; 
  face2d[2] = m_inverse * p2;
  face2d[3] = m_inverse * p3;

  // print & draw as you did before...

}
+1

v0-v1-v3-v2 v3-v0, v3-v2 , 2d- .

. ( , ) . 3d / ​​:

vx.x    vx.y    vx.z    0
vy.x    vy.y    vy.z    0
vz.x    vz.y    vz.z    0
vp.x    vp.y    vp.z    1

vx - x , vy - y, vz - z vp - .

, v3-v0 y (2- ), v3-v2-x (1- ) -z (3- ). . . , 2d .

3d-, 2- .

, - , , .

0

: (: "" "" )

  • , , .
    • .
    • .
    • .
    • .
    • .
    • 1.
    • .
  • .
    • , , (, ).
    • .
  • For each vertex v of the face, multiply it by two matrices: v * view * projection.

The result is a projection of your three-dimensional faces onto a 2d space, as if you were looking at them exactly orthogonally without any promising disturbances. The final coordinates will be in the normalized coordinates of the screen, where (-1, -1) is the lower left corner, (0, 0) is the center and (1, 1) is the upper right corner.

0
source

Source: https://habr.com/ru/post/1755075/

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