n次ベジェ曲線を実装する

n_bezierCurve.pde

//SFC17「CGとCADの数理」で出たn次ベジェ曲線を実装する課題
//本当はaddDegreeとかやりたくない、addPointだけでやりたいから時間が出来たらやる
//コメントがめんどくさいのであとでやる

class BezierCurve {
  ArrayList<Integer> Px = new ArrayList<Integer>();
  ArrayList<Integer> Py = new ArrayList<Integer>();
  PVector[] R;
  int tn;
  int n;  //degree

  BezierCurve() {   //constructor 
    tn = 20;
    R = new PVector[tn];
    n = 1;
  } 

  void addPoint(int x, int y) {
    Px.add(x);
    Py.add(y);
  }

  void addDegree(int degree) {
    n = degree;
  }

  void draw() {
    int   tt;
    float t = 0.0;
    float ts = (float)1 / tn;
    float[] Bt = new float[n+1];

    int[] coefData = {1, 1,1, 1,2,1, 1,3,3,1, 1,4,6,4,1, 1,5,10,10,5,1, 1,6,15,20,15,6,1, 1,7,21,35,35,21,7,1, 1,8,28,56,70,56,28,8,1, 1,9,36,84,126,126,84,36,9,1};
    int[] coef = new int[n+1];
    int begin = 0;

    for (int k = 1; k <= n; k++) {
      begin += k;
    }

    for (int k = 0; k <= n; k++) {
      coef[k] = coefData[begin+k];
    }

    stroke(0, 255, 255);
    fill(0, 255, 255, 30);

    for (int k = 0; k < n; k++) {
      line(Px.get(k), Py.get(k), Px.get(k+1), Py.get(k+1));
    }
    line(Px.get(n), Py.get(n), Px.get(0), Py.get(0));

    for (int k = 0; k < n+1; k++) {
      fill(0, 255, 255);
      ellipse(Px.get(k), Py.get(k), 10, 10);
      fill(255, 255, 255);
      text('P' + k, Px.get(k), Py.get(k));
    }

    noFill();
    stroke(255, 255, 255);
    for (tt = 0; tt < tn; tt += 1) {
      for (int k = 0; k < n+1; k++) {
        Bt[k] = 1.0;
      }
      for (int k = 0; k < n+1; k++) {
        Bt[k] = (float)coef[k];
        for (int j = 0; j < k; j++) Bt[k] = Bt[k] * t;
        for (int l = 0; l < n-k; l++) Bt[k] = Bt[k] * (1-t);
      }

      R[tt] = new PVector();
      R[tt].x = 0.0;
      R[tt].y = 0.0;

      for (int g = 0; g < n+1; g++) {
        R[tt].x += Px.get(g) * Bt[g];
        R[tt].y += Py.get(g) * Bt[g];
      }
      if (tt != 0) {
        line(R[tt-1].x, R[tt-1].y, R[tt].x, R[tt].y);
      }
      t = t + ts;
    }
    line(R[tt-1].x, R[tt-1].y, Px.get(n), Py.get(n));
  }
}

BezierCurve b0;

void setup() {
  size(400, 400);
  b0 = new BezierCurve();

  int[] px = new int[9];
  int[] py = new int[9];

  px[0] =  20; py[0] = 300;
  px[1] = 140; py[1] = 100;
  px[2] = 280; py[2] = 100;
  px[3] = 380; py[3] = 300;
  px[4] = 300; py[4] = 300;
  px[5] = 280; py[5] = 200;
  px[6] = 150; py[6] = 180;
  px[7] = 140; py[7] = 170;
  px[8] = 130; py[8] = 300;

  for (int i = 0; i < 8; i++) {
    b0.addPoint(px[i], py[i]);
  }
  b0.addDegree(7);  //input degree
}

void draw() {
  background(40);

  text("BezierCurve", 10, 20);

  b0.draw();

  stop();
}