Circle tagents

[sessionbeer 10]

Goal:


Looking into tangent lines between two circles and trying to convert this function into vex.
 

The code is originally in Java but looks like it should be easily converted to vex but I'm getting errors with my attempt below. 
 

function float[] common_tangent_line(x1, y1, r1, x2, y2, r2) {
  // Compute the common tangent line of two circles: (x1, y1) - r1 and (x2, y2) - r2
  // Return in the form of line equation: ax + by + c == 0
  delta1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 + r2) * (r1 + r2);
  delta2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 - r2) * (r1 - r2);
  p1 = r1 * (x1 * x2 + y1 * y2 - x2 * x2 - y2 * y2);
  p2 = r2 * (x1 * x1 + y1 * y1 - x1 * x2 - y1 * y2);
  q = x1 * y2 - x2 * y1;
  results = [];
  if(delta1 >= 0) {
    l11 = {
      a: (x2 - x1) * (r1 + r2) + (y1 - y2) * Math.sqrt(delta1),
      b: (y2 - y1) * (r1 + r2) + (x2 - x1) * Math.sqrt(delta1),
      c: p1 + p2 + q * Math.sqrt(delta1)
    };
    l12 = {
      a: (x2 - x1) * (r1 + r2) - (y1 - y2) * Math.sqrt(delta1),
      b: (y2 - y1) * (r1 + r2) - (x2 - x1) * Math.sqrt(delta1),
      c: p1 + p2 - q * Math.sqrt(delta1)
    };
    results.push(l11);
    results.push(l12);
  }
  if(delta2 >= 0) {
    l21 = {
      a: (x2 - x1) * (r1 - r2) + (y1 - y2) * Math.sqrt(delta2),
      b: (y2 - y1) * (r1 - r2) + (x2 - x1) * Math.sqrt(delta2),
      c: p1 - p2 + q * Math.sqrt(delta2)
    };
    l22 = {
      a: (x2 - x1) * (r1 - r2) - (y1 - y2) * Math.sqrt(delta2),
      b: (y2 - y1) * (r1 - r2) - (x2 - x1) * Math.sqrt(delta2),
      c: p1 - p2 - q * Math.sqrt(delta2)
    };
    results.push(l21);
    results.push(l22);
  }
  return results;
}

 

Edited August 2 by sessionbeer

[animatrix 300]

Hi,

You also have to change the function calls like:

Math.sqrt(delta1)

results.push(l21)

to:

sqrt(delta1)

push(results, l21)

 

[sessionbeer 10]

Thanks! I'm getting an error with the first line:

function float[] common_tangent_line(x1, y1, r1, x2, y2, r2) {
....
}

Error: Syntax error, unexpected ',', expecting identifies (1,40).

[animatrix 300]

You have to specify the type for the arguments:

function float[] common_tangent_line(float x1, y1, r1, x2, y2, r2) {

}

 

[sessionbeer 10]

Great, thank you. Last one:
How do I correct the error for a: ?

if(delta1 >= 0) {
    l11 = {
      a: = (x2 - x1) * (r1 + r2) + (y1 - y2) * sqrt(delta1),
      b: (y2 - y1) * (r1 + r2) + (x2 - x1) * sqrt(delta1),
      c: p1 + p2 + q * sqrt(delta1)
    };

 

[fencer 203]

11 hours ago, sessionbeer said:

Great, thank you. Last one:
How do I correct the error for a: ?

if(delta1 >= 0) {
    l11 = {
      a: = (x2 - x1) * (r1 + r2) + (y1 - y2) * sqrt(delta1),
      b: (y2 - y1) * (r1 + r2) + (x2 - x1) * sqrt(delta1),
      c: p1 + p2 + q * sqrt(delta1)
    };

 

Looks like homework wasn't done first

 

[sessionbeer 10]

Really hard to do the right homework when you don't know the right questions to ask 

Edited August 1 by sessionbeer

[sessionbeer 10]

Getting no more errors but seems like the results are incorrect. I've made a @common attribute to hold the results which I'm expecting to be (a,b,c) but instead, I'm getting a lot more float values. Attached a hip file too to show all the errors in my ways.
 

function float[] common_tangent_line(float x1, y1, r1, x2, y2, r2) {
  // Compute the common tangent line of two circles: (x1, y1) - r1 and (x2, y2) - r2
  // Return in the form of line equation: ax + by + c == 0
  float delta1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 + r2) * (r1 + r2);
  float delta2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 - r2) * (r1 - r2);
  float p1 = r1 * (x1 * x2 + y1 * y2 - x2 * x2 - y2 * y2);
  float p2 = r2 * (x1 * x1 + y1 * y1 - x1 * x2 - y1 * y2);
  float q = x1 * y2 - x2 * y1;
  float results[];
  
  if(delta1 >= 0) {
    float a = (x2 - x1) * (r1 + r2) + (y1 - y2) * sqrt(delta1);
    float b = (y2 - y1) * (r1 + r2) + (x2 - x1) * sqrt(delta1);
    float c = p1 + p2 + q * sqrt(delta1);
    float   l11[];
    l11 = array(a,b,c);

    float a2 = (x2 - x1) * (r1 + r2) - (y1 - y2) * sqrt(delta1);
    float b2 = (y2 - y1) * (r1 + r2) - (x2 - x1) * sqrt(delta1);
    float c2 = p1 + p2 - q * sqrt(delta1);
    float   l12[];
    l12 = array(a,b,c);
    push(results, l11);
    push(results, l12);
  };
  if(delta2 >= 0) {
    float a = (x2 - x1) * (r1 - r2) + (y1 - y2) * sqrt(delta2);
    float b = (y2 - y1) * (r1 - r2) + (x2 - x1) * sqrt(delta2);
    float c = p1 - p2 + q * sqrt(delta2);
    float   l21[];
    l21 = array(a,b,c);

    float a2 = (x2 - x1) * (r1 - r2) - (y1 - y2) * sqrt(delta2);
    float b2 = (y2 - y1) * (r1 - r2) - (x2 - x1) * sqrt(delta2);
    float c2 = p1 - p2 - q * sqrt(delta2);
    float   l22[];
    l22 = array(a,b,c);
    push(results, l21);
    push(results, l22);
  }
  return results;
}

vector point1 = @P;;
vector point2 = (0,"P",1);

f[]@common =  common_tangent_line(point1.x, point1.y, 1.5, point2.x, point2.y, 1);

 

Circle_Tangents_03.hip

Edited August 1 by sessionbeer

[fencer 203]

10 hours ago, sessionbeer said:

Getting no more errors but seems like the results are incorrect. I've made a @common attribute to hold the results which I'm expecting to be (a,b,c) but instead, I'm getting a lot more float values. Attached a hip file too to show all the errors in my ways.
 

function float[] common_tangent_line(float x1, y1, r1, x2, y2, r2) {
  // Compute the common tangent line of two circles: (x1, y1) - r1 and (x2, y2) - r2
  // Return in the form of line equation: ax + by + c == 0
  float delta1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 + r2) * (r1 + r2);
  float delta2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) - (r1 - r2) * (r1 - r2);
  float p1 = r1 * (x1 * x2 + y1 * y2 - x2 * x2 - y2 * y2);
  float p2 = r2 * (x1 * x1 + y1 * y1 - x1 * x2 - y1 * y2);
  float q = x1 * y2 - x2 * y1;
  float results[];
  
  if(delta1 >= 0) {
    float a = (x2 - x1) * (r1 + r2) + (y1 - y2) * sqrt(delta1);
    float b = (y2 - y1) * (r1 + r2) + (x2 - x1) * sqrt(delta1);
    float c = p1 + p2 + q * sqrt(delta1);
    float   l11[];
    l11 = array(a,b,c);

    float a2 = (x2 - x1) * (r1 + r2) - (y1 - y2) * sqrt(delta1);
    float b2 = (y2 - y1) * (r1 + r2) - (x2 - x1) * sqrt(delta1);
    float c2 = p1 + p2 - q * sqrt(delta1);
    float   l12[];
    l12 = array(a,b,c);
    push(results, l11);
    push(results, l12);
  };
  if(delta2 >= 0) {
    float a = (x2 - x1) * (r1 - r2) + (y1 - y2) * sqrt(delta2);
    float b = (y2 - y1) * (r1 - r2) + (x2 - x1) * sqrt(delta2);
    float c = p1 - p2 + q * sqrt(delta2);
    float   l21[];
    l21 = array(a,b,c);

    float a2 = (x2 - x1) * (r1 - r2) - (y1 - y2) * sqrt(delta2);
    float b2 = (y2 - y1) * (r1 - r2) - (x2 - x1) * sqrt(delta2);
    float c2 = p1 - p2 - q * sqrt(delta2);
    float   l22[];
    l22 = array(a,b,c);
    push(results, l21);
    push(results, l22);
  }
  return results;
}

vector point1 = @P;;
vector point2 = (0,"P",1);

f[]@common =  common_tangent_line(point1.x, point1.y, 1.5, point2.x, point2.y, 1);

 

Circle_Tangents_03.hip

Well done. Check hip, I have added the rest code from the article above. Hope it will help to finish the setup.

cg_v01.hip

Edited August 1 by fencer

[sessionbeer 10]

Thanks for all the helpful tips, I got it working finally