geometry in 3d

geometry-3d.js

v3 = new function() {
  this.forward = [0,0,1]
  this.up = [0,1,0]
  this.right = [1,0,0]
  this.zero = [0,0,0]
}

// rotate vector
rotvec = function(vec,axis,th){
  var [l,m,n] = axis
  var [x,y,z] = vec
  var [costh,sinth] = [Math.cos(th), Math.sin(th)]
  var mat={}
  mat[11]= l*l *(1-costh) +costh
  mat[12]= m*l *(1-costh) -n*sinth
  mat[13]= n*l *(1-costh) +m*sinth

  mat[21]= l*m *(1-costh) +n*sinth
  mat[22]= m*m *(1-costh) +costh
  mat[23]= n*m *(1-costh) -l*sinth

  mat[31]= l*n *(1-costh) -m*sinth
  mat[32]= m*n *(1-costh) +l*sinth
  mat[33]= n*n *(1-costh) +costh
  return [
    x*mat[11] + y*mat[12] + z*mat[13],
    x*mat[21] + y*mat[22] + z*mat[23],
    x*mat[31] + y*mat[32] + z*mat[33],
  ]
}

roteuler = function(vec,rot){
  if (rot.z != 0) {vec = v3.rotvec(vec,v3.forward,rot.z)}
  if (rot.x != 0) {vec = v3.rotvec(vec,v3.right,rot.x)}
  if (rot.y != 0) {vec = v3.rotvec(vec,v3.up,rot.y)}
  return vec
}

scale = function(vec,p){
  return [vec.x*p,vec.y*p,vec.z*p]
}

copy = function(v0){
  return [v0.x,v0.y,v0.z]
}

add = function(v0,v){
  return [v0.x+v.x,v0.y+v.y,v0.z+v.z]
}

subtract = function(v0,v){
  return [v0.x-v.x,v0.y-v.y,v0.z-v.z]
}

// magnitude
mag = function(v){
  return Math.sqrt(v.x*v.x + v.y*v.y + v.z*v.z)
}

normalize = function(v){
  p = 1/mag(v)
  return [v.x*p,v.y*p,v.z*p]
}

dot = function(u,v){
  return u.x*v.x + u.y*v.y + u.z*v.z 
}

cross = function(u,v){
  return [
    u.y*v.z - u.z*v.y,
    u.z*v.x - u.x*v.z,
    u.x*v.y - u.y*v.x
  ]
}

angcos = function(u,v){
  return v3.dot(u,v)/(v3.mag(u)*v3.mag(v))
}

ang = function(u,v){
  return Math.acos(v3.angcos(u,v))
}

toeuler = function(v0){
  var ep = 5
  var ma = 2*PI
  var mr = [0,0,0]
  var cnt = 0
  for (var x = -180; x < 180; x+=ep){
    for (var y = -90; y < 90; y+=ep){
      cnt ++;
      var r = [rad(x),rad(y),0]
      var v = v3.roteuler([0,0,1],r)
      var a = v3.ang(v0,v)
      if (a < rad(ep)){
        return r
      }
      if (a < ma){
        ma = a
        mr = r
      }
    }
  }
  return mr
}

lerp = function(u,v,p){
  return [
    u.x*(1-p)+v.x*p,
    u.y*(1-p)+v.y*p,
    u.z*(1-p)+v.z*p,
  ]
}