Flower Bezier curves

Managed to lose my Bezier demo (Flower/Spiral generator) in November - (damn you 'Time Machine') - Actually, it turned out to be a good thing, as it made me rethink the maths - in terms of Vectors rather than equations of straight lines. The four control points for the cubic bezier are calculated by working out the tangents to lines radiating from the centre of a circle. Using the radius line and its tangent - we work out an orthogonal matrix - applying a 'tilt' (rotation matrix) to squash or expand the petal.
My lost code was horrible - all sorts of case statements to deal with angle quadrants.


The following code - is the very start of my new Demo program

int displayWidth,displayHeight ;
String mode ;
float CX,CY ;


  float degreesToRadians(float th) 
  {
    return PI * th /180.0f ;  
  }



  float translateX(float x) 
  {
    return x+CX ;
  }
  

  float translateY(float y) 
  {
    return -y+displayHeight-CY ;   
  }
  

  PVector [] calcControlPoints(float angle,float ro,float radius,float tilt,float petalLength) 
  {
  
    PVector [] bezControlPoints = new PVector[4] ;
  
    float halfRo = ro / 2.0f ;
  
    PVector[] cPoints = calcPetalPointPair(angle-halfRo,tilt,petalLength) ;
    PVector startPt = cPoints[0] ;
    PVector fPoint = cPoints[1] ;

  
    bezControlPoints[0] = new PVector(startPt.x * radius,startPt.y * radius) ;
    bezControlPoints[1] = new PVector(startPt.x * radius + fPoint.x,startPt.y * radius + fPoint.y) ;
  


    PVector [] cPoints2 = calcPetalPointPair(angle+halfRo,-tilt,petalLength) ;
    startPt = cPoints2[0] ;
    fPoint = cPoints2[1] ;
  
    bezControlPoints[3] = new PVector(startPt.x * radius,startPt.y * radius) ;
    bezControlPoints[2] = new PVector(startPt.x * radius + fPoint.x,startPt.y * radius + fPoint.y) ;
 

    return bezControlPoints ;  
    
  }
  
  
  void drawBezier(PVector [] cps) 
  {
    drawBezier(cps[0].x,cps[0].y,cps[1].x,cps[1].y,cps[2].x,cps[2].y,cps[3].x,cps[3].y) ;
  }
  
  void drawBezier(float x1,float y1,float x2,float y2,float x3,float y3,float x4,float y4) 
  {
    noFill() ;
    stroke(0,0,0) ;
    bezier(translateX(x1),translateY(y1),
      translateX(x2),translateY(y2),
      translateX(x3),translateY(y3),
      translateX(x4),translateY(y4)) ;
    

    
  }
  
  
  void drawControlPoints(PVector[] cps) 
  {
    stroke(255,0,0) ;
    drawLine(cps[0].x,cps[0].y,cps[1].x,cps[1].y) ;
    stroke(0,255,0) ;
    drawLine(cps[2].x,cps[2].y,cps[3].x,cps[3].y) ;
      
  }
  
  
  
  PVector[] calcPetalPointPair(float angle,float tilt,float petalLength)
  {
 
    
    PVector startPt = new PVector(1.0*sin(degreesToRadians(angle)),1.0*cos(degreesToRadians(angle)));


    PVector vert = new PVector(0,0,1.0f) ;      // Unit Vector Perp to XY Plane
    PVector nCPc = startPt.cross(vert) ;        // Calculate Tangent to Circle at startPt.x,startPt.y
  
  
    PMatrix2D iMat = new PMatrix2D() ;
  
    iMat.rotate(degreesToRadians(tilt < 0 ? 180+tilt : tilt)) ;    // Petal Tilt

  
    PMatrix2D cMat = new PMatrix2D(nCPc.x,startPt.x,0f,nCPc.y,startPt.y,0.0f) ;
  
  // Matrix 
  // | nCPc.x  startx |
  // | nCPc.y  starty |
  
  
    cMat.preApply(iMat) ;      // Apply our orthog axis to the rotation matrix 
  
  
    PVector fPoint = new PVector() ;
    PVector sPoint = new PVector(petalLength,0) ;    // Petal Length
  
    cMat.mult(sPoint,fPoint) ;            // Apply Full transformation to petal Vector
   
    PVector [] points = new PVector[2] ;
    points[0] = startPt ;
    points[1] = fPoint ;
 
    return points;
  
 }
 
    



  void setup() 
  {
  
    mode = JAVA2D ;
  
  
    displayHeight = screen.height/2 ;
    displayWidth = screen.width/2 ;
    CX = displayWidth / 2 ;
    CY = displayHeight / 2 ;
  
    size(displayWidth, displayHeight,mode);
    loop() ;
  
  }
  
  void drawLine(float x,float y,float x2,float y2) {
    line(translateX(x),translateY(y),translateX(x2),translateY(y2)) ;
  }

  void drawCircle(float x,float y,float rad) 
  {
     ellipse(translateX(x), translateY(y), rad,rad) ;
  }




  void draw() {

    background(255);
    float dt = 1/frameRate ;    // We should calculate dt - time passed since last update-draw

    float radius = 20.0f ;
    float tilt = 70.0f ;
    float petalLength = 250.0f ;
    float ro = 15.0f ;  
    float step = 7.0f ;
    float numpetals = 360.0f / step  ;
      
    noFill() ;
    ellipseMode(RADIUS) ;
    stroke(0,0,0) ;
    drawCircle(0,0,radius) ;
    
    for (float angle = 0.0f ; angle < step*numpetals ; angle+=step) 
    {
      PVector [] cps = calcControlPoints(angle,ro,radius,tilt,petalLength) ;
          drawBezier(cps) ;
    }


     
            
  }