java-处理浮点数舍入误差，如何保持弧度有理

Question

我已经修改了这个 arcball class 以便每次调用 arcball.rollforward(PI/180);将矩阵旋转 1 度。我试图设置它，因此 arcball.rollback() 被调用时使用累积的浮点数 rotatebywithincludedfloaterror 但它具有与回滚 360 度相同的度数错误而没有浮点数错误。这是 1000 次完整旋转后它偏离的距离，它应该是顶部立方体在 x

上的 1:1 反射

这里是 main 函数，带有 1 * 360 度旋转循环和用于测试的帧率（将多次旋转的帧率设置为 900，这样它就不会花很长时间）

Arcball arcball;

int i;

//framecount
int fcount, lastm;
float frate;
int fint = 3;

boolean[] keys = new boolean[13];
    final int w = 0;


void setup() {
  size(900, 700, P3D); 
  frameRate(60);
  noStroke();
  arcball = new Arcball(width/2, height/2, 100);   //100 is radius
}

void draw() {
  lights();
  background(255,160,122);
  
  print(" \n degree = " + i );
  i++;
  if(i <= (360 * 1)) { arcball.rollforward(PI/180); }
  else { print(" break"); }
  
  if(keys[w]) { arcball.rollforward(PI/180); }

  translate(width/2, height/2-100, 0);
  box(50);
   
  translate(0, 200, 0);
  arcball.run();
  box(50);  
  
  
  fcount += 1;
  int m = millis();
  if (m - lastm > 1000 * fint) {
    frate = float(fcount) / fint;
    fcount = 0;
    lastm = m;
    println("fps: " + frate);
  }
                           
}

void keyPressed() {
  switch(key) {
    case 119: 
        keys[w] = true;
        break;
  }
}
void keyReleased() {
  switch(key) {
    case 119: 
        keys[w] = false;
        break;
    } 
}

和弧线球class

// Ariel and V3ga's arcball class with a couple tiny mods by Robert Hodgin and smaller mods by cubesareneat

class Arcball {
  float center_x, center_y, radius;
  Vec3 v_down, v_drag;
  Quat q_now, q_down, q_drag;
  Vec3[] axisSet;
  int axis;
  float mxv, myv;
  float x, y;
  
  float degreeW_count = 0;
  float degreeS_count = 0;
  float rotatebywithincludedfloaterror =0;
  
  Arcball(float center_x, float center_y, float radius){
    this.center_x = center_x;
    this.center_y = center_y;
    this.radius = radius;

    v_down = new Vec3();
    v_drag = new Vec3();

    q_now = new Quat();
    q_down = new Quat();
    q_drag = new Quat();

    axisSet = new Vec3[] {new Vec3(1.0f, 0.0f, 0.0f), new Vec3(0.0f, 1.0f, 0.0f), new Vec3(0.0f, 0.0f, 1.0f)};
    axis = -1;  // no constraints...    
  }

  void rollforward(float radians2turn) { 
    rotatebywithincludedfloaterror = rotatebywithincludedfloaterror + (-1 * (((sin(radians2turn) * radius))/2));
    if(degreeW_count >= 360) {
      arcball.rollback(rotatebywithincludedfloaterror);
      degreeW_count = 0;
      rotatebywithincludedfloaterror = 0;
    }
    rollortilt(0, -1 * (((sin(radians2turn) * radius))/2)); 
    degreeW_count = degreeW_count + 1; // need to edit this later to work with rotations other then 1 degree
  }
  void rollback(float radians2turn) { 
    rollortilt(0, ((sin(radians2turn) * radius))/2);
  }
  
  void rollortilt(float xtra, float ytra){
    q_down.set(q_now);
    v_down = XY_to_sphere(center_x, center_y);
    q_down.set(q_now);
    q_drag.reset();
    
    v_drag = XY_to_sphere(center_x + xtra, center_y + ytra);
    q_drag.set(Vec3.dot(v_down, v_drag), Vec3.cross(v_down, v_drag)); 
  }

/*
  void mousePressed(){
    v_down = XY_to_sphere(mouseX, mouseY);  
    q_down.set(q_now);
    q_drag.reset();
  }

  void mouseDragged(){
    v_drag = XY_to_sphere(mouseX, mouseY);
    q_drag.set(Vec3.dot(v_down, v_drag), Vec3.cross(v_down, v_drag));
  }
*/
  void run(){
    q_now = Quat.mul(q_drag, q_down);
    applyQuat2Matrix(q_now);
    
    x += mxv;
    y += myv;
    mxv -= mxv * .01;
    myv -= myv * .01;
  }
  
  Vec3 XY_to_sphere(float x, float y){
    Vec3 v = new Vec3();
    v.x = (x - center_x) / radius;
    v.y = (y - center_y) / radius;

    float mag = v.x * v.x + v.y * v.y;
    if (mag > 1.0f){
      v.normalize();
    } else {
      v.z = sqrt(1.0f - mag);
    }

    return (axis == -1) ? v : constrain_vector(v, axisSet[axis]);
  }

  Vec3 constrain_vector(Vec3 vector, Vec3 axis){
    Vec3 res = new Vec3();
    res.sub(vector, Vec3.mul(axis, Vec3.dot(axis, vector)));
    res.normalize();
    return res;
  }

  void applyQuat2Matrix(Quat q){
    // instead of transforming q into a matrix and applying it...

    float[] aa = q.getValue();
    rotate(aa[0], aa[1], aa[2], aa[3]);
  }
}

static class Vec3{
  float x, y, z;

  Vec3(){
  }

  Vec3(float x, float y, float z){
    this.x = x;
    this.y = y;
    this.z = z;
  }

  void normalize(){
    float length = length();
    x /= length;
    y /= length;
    z /= length;
  }

  float length(){
    return (float) Math.sqrt(x * x + y * y + z * z);
  }

  static Vec3 cross(Vec3 v1, Vec3 v2){
    Vec3 res = new Vec3();
    res.x = v1.y * v2.z - v1.z * v2.y;
    res.y = v1.z * v2.x - v1.x * v2.z;
    res.z = v1.x * v2.y - v1.y * v2.x;
    return res;
  }

  static float dot(Vec3 v1, Vec3 v2){
    return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;
  }
  
  static Vec3 mul(Vec3 v, float d){
    Vec3 res = new Vec3();
    res.x = v.x * d;
    res.y = v.y * d;
    res.z = v.z * d;
    return res;
  }

  void sub(Vec3 v1, Vec3 v2){
    x = v1.x - v2.x;
    y = v1.y - v2.y;
    z = v1.z - v2.z;
  }
}

static class Quat{
  float w, x, y, z;

  Quat(){
    reset();
  }

  Quat(float w, float x, float y, float z){
    this.w = w;
    this.x = x;
    this.y = y;
    this.z = z;
  }

  void reset(){
    w = 1.0f;
    x = 0.0f;
    y = 0.0f;
    z = 0.0f;
  }

  void set(float w, Vec3 v){
    this.w = w;
    x = v.x;
    y = v.y;
    z = v.z;
  }

  void set(Quat q){
    w = q.w;
    x = q.x;
    y = q.y;
    z = q.z;
  }

  static Quat mul(Quat q1, Quat q2){
    Quat res = new Quat();
    res.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z;
    res.x = q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y;
    res.y = q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z;
    res.z = q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x;
    return res;
  }
  
  float[] getValue(){
    // transforming this quat into an angle and an axis vector...

    float[] res = new float[4];

    float sa = (float) Math.sqrt(1.0f - w * w);
    if (sa < EPSILON){
      sa = 1.0f;
    }

    res[0] = (float) Math.acos(w) * 2.0f;
    res[1] = x / sa;
    res[2] = y / sa;
    res[3] = z / sa;
    return res;
  }
}

跟踪浮动误差范围 return 相同的度数 arcball.rollforward()

  void rollforward(float radians2turn) { 
    rotatebywithincludedfloaterror = rotatebywithincludedfloaterror + (-1 * (((sin(radians2turn) * radius))/2));
    if(degreeW_count >= 360) {
      arcball.rollback(rotatebywithincludedfloaterror);
      degreeW_count = 0;
      rotatebywithincludedfloaterror = 0;
    }
    rollortilt(0, -1 * (((sin(radians2turn) * radius))/2)); 
    degreeW_count = degreeW_count + 1; // need to edit this later to work with rotations other then 1 degree
  }

Answer 1

在问题中使用我的想法每 2*PI 重置一次

  if(keys[w]) { 
    arcball.rollforward(PI/180);
    degreeW_count = degreeW_count + 1;
  }

  if(degreeW_count == 360) {
    arcball = new Arcball(width/2, height/2, 100); // setset to original arcball at 0 degrees
    degreeW_count = 0;
  }

弧球

  void rollforward(float degrees2turn) { 
    rollortilt(0, -1 * (((sin(degrees2turn) * radius))/2));  // one degree forward 180/PI
  }

这完全避免了任何使用无理数和周期函数的数据类型会累积的舍入误差！

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