// but still not found the ERROR

​

var d = 7;

var x1 = 80, y1 = 60;

var x2 = 250,y2 = 30;

// mouse point for circum_circle play

var x3 = 350,y3 = 250; // about if y3 < y1 ERROR in calc

var L12, L23, L31, All, A1, A2, A3, M12x, M12y, M23x, M23y, M31x, M31y;

var CR, CRx, CRy, CRA, MR;

var outtxt = "";

​

function setup() {

  createCanvas(500, 500);

  link_info();

}

​

function draw() {

  background(120, 120, 0);

  draw_points();

  calc_circle();

  draw_circum_circle();

  text_info();

}

​

function draw_points() {

  stroke(0);

  noFill();

  circle(x1, y1, d);

  text("1", x1 + 3, y1 - 3);

  circle(x2, y2, d);

  text("2", x2 + 3, y2 - 3);

  x3 = mouseX;

  y3 = mouseY;

  circle(x3, y3, d);

  text("3", x3 + 3, y3 - 3);

  stroke(0,0,200);

  triangle(x1, y1, x2, y2, x3, y3);

}

​

function calc_circle() {

  L12 = dist(x1, y1, x2, y2);

  L23 = dist(x2, y2, x3, y3);

  L31 = dist(x1, y1, x3, y3);

  // now that is a SSS triangle, calc the angles

  //A1 = acos((sq(L12) + sq(L31) - sq(L23)) / (2 * L12 * L31));

  A2 = acos((sq(L12) + sq(L23) - sq(L31)) / (2 * L12 * L23));

  //A3 = acos((sq(L23) + sq(L31) - sq(L12)) / (2 * L23 * L31));

  //All = A1+A2+A3;

  // calc middle points 

  //  M12x = x1 + (x2 - x1) / 2;

  //  M12y = y1 + (y2 - y1) / 2;

  //  M23x = x2 + (x3 - x2) / 2;

  //  M23y = y2 + (y3 - y2) / 2;

  M31x = x3 + (x1 - x3) / 2;

  M31y = y3 + (y1 - y3) / 2;

  //the common angle of departure being 90° minus the angle of the opposite vertex

  // for CR must be: L31/2 = CR*cos(90-A2);

  //CR = L31 / 2 / cos(HALF_PI-A2);

  // now read WIKI:  sinus law! 2CR = L31/sin(A2) 

  CR = L31 / 2 / sin(A2);

  //  MR = CR * sin(HALF_PI - A2);

  CRA = acos((x3 - x1) / L31) - (HALF_PI - A2); // angle p1 p3 line - ( 90 - p2 angle)

  CRx = x1 + CR * cos(CRA);

  CRy = y1 + CR * sin(CRA);

}

​

function draw_circum_circle() {

  stroke(255, 0, 0);            // midpoints

  //  ellipse(M12x, M12y, r, r);

  //  ellipse(M23x, M23y, r, r);

  circle(M31x, M31y, d);

  stroke(255, 0, 0);

  fill(130, 130, 0);

  triangle(x1, y1, CRx, CRy, M31x, M31y); // one of 6 magic triangles what rule the circum circle

  noFill();

  stroke(200, 200, 0);           // yellow 

  circle(CRx, CRy, 2 * CR);      // circum circle

  circle(CRx, CRy, d);           // centerpoint

}

​

function text_info() {

  noStroke();

  fill(255);

  outtxt  = " CR: "      + nf(CR, 0, 1);

  outtxt += " , CRA: "   + nf(degrees(CRA), 0, 1);

  outtxt += " deg, CRx " + nf(CRx, 0, 0);

  outtxt += " , CRy "    + nf(CRy, 0, 0);

  text(outtxt, 10, height - 10);

  outtxt  = " L12: "     + nf(L12, 0, 0);

  outtxt += " , L23: "   + nf(L23, 0, 0);

  outtxt += " , L31: "   + nf(L31, 0, 0);

  outtxt += " , x3: "    + nf(x3,  0, 0);

  outtxt += " , y3: "    + nf(y3,  0, 0);

//  outtxt += " , A1: "    + nf(degrees(A1), 0, 1) + " deg ";

  outtxt += " , A2: "    + nf(degrees(A2), 0, 1) + " deg ";

//  outtxt += " , A3: "    + nf(degrees(A3), 0, 1) + " deg ";

//  outtxt += " , All: "    + nf(degrees(All), 0, 1) + " deg ";

  text(outtxt, 10, 14);

}

​

function link_info() {

  print(" org: https://editor.p5js.org/kll/sketches/rkRiXYYh7");

  print(" math: https://en.wikipedia.org/wiki/Circumscribed_circle");

  print(" wiki: https://en.wikipedia.org/wiki/Law_of_sines");

  print(" forum: https://discourse.processing.org/t/circumcircle-of-triangle/13030");

}

​

​

/*

// processing 3.5.3 JAVA MODE version 

​

int d = 7;

int x1 = 80, y1 = 60;

int x2 = 250,y2 = 30;

// mouse point for circum_circle play

float x3 = 350,y3 = 250; // about if y3 < y1 ERROR in calc

float L12, L23, L31, All, A1, A2, A3, M12x, M12y, M23x, M23y, M31x, M31y;

float CR, CRx, CRy, CRA, MR;

String outtxt = "";

​

void setup() {

  size(500, 500);

  link_info();

}

​

void draw() {

  background(120, 120, 0);

  draw_points();

  calc_circle();

  draw_circum_circle();

  text_info();

}

​

void draw_points() {

  stroke(0);

  noFill();

  circle(x1, y1, d);

  text("1", x1 + 3, y1 - 3);

  circle(x2, y2, d);

  text("2", x2 + 3, y2 - 3);

  x3 = mouseX;

  y3 = mouseY;

  circle(x3, y3, d);

  text("3", x3 + 3, y3 - 3);

  stroke(0,0,200);

  triangle(x1, y1, x2, y2, x3, y3);

}

​

void calc_circle() {

  L12 = dist(x1, y1, x2, y2);

  L23 = dist(x2, y2, x3, y3);

  L31 = dist(x1, y1, x3, y3);

  // now that is a SSS triangle, calc the angles

  //A1 = acos((sq(L12) + sq(L31) - sq(L23)) / (2 * L12 * L31));

  A2 = acos((sq(L12) + sq(L23) - sq(L31)) / (2 * L12 * L23));

  //A3 = acos((sq(L23) + sq(L31) - sq(L12)) / (2 * L23 * L31));

  //All = A1+A2+A3;

  // calc middle points 

  //  M12x = x1 + (x2 - x1) / 2;

  //  M12y = y1 + (y2 - y1) / 2;

  //  M23x = x2 + (x3 - x2) / 2;

  //  M23y = y2 + (y3 - y2) / 2;

  M31x = x3 + (x1 - x3) / 2;

  M31y = y3 + (y1 - y3) / 2;

  //the common angle of departure being 90° minus the angle of the opposite vertex

  // for CR must be: L31/2 = CR*cos(90-A2);

  //CR = L31 / 2 / cos(HALF_PI-A2);

  // now read WIKI:  sinus law! 2CR = L31/sin(A2) 

  CR = L31 / 2 / sin(A2);

  //  MR = CR * sin(HALF_PI - A2);

  CRA = acos((x3 - x1) / L31) - (HALF_PI - A2); // angle p1 p3 line - ( 90 - p2 angle)

  CRx = x1 + CR * cos(CRA);

  CRy = y1 + CR * sin(CRA);

}

​

void draw_circum_circle() {

  stroke(255, 0, 0);            // midpoints

  //  ellipse(M12x, M12y, r, r);

  //  ellipse(M23x, M23y, r, r);

  circle(M31x, M31y, d);

  stroke(255, 0, 0);

  fill(130, 130, 0);

  triangle(x1, y1, CRx, CRy, M31x, M31y); // one of 6 magic triangles what rule the circum circle

  noFill();

  stroke(200, 200, 0);           // yellow 

  circle(CRx, CRy, 2 * CR);      // circum circle

  circle(CRx, CRy, d);           // centerpoint

}

​

void text_info() {

  noStroke();

  fill(255);

  outtxt  = " CR: "      + nf(CR, 0, 1);

  outtxt += " , CRA: "   + nf(degrees(CRA), 0, 1);

  outtxt += " deg, CRx " + nf(CRx, 0, 0);

  outtxt += " , CRy "    + nf(CRy, 0, 0);

  text(outtxt, 10, height - 10);

  outtxt  = " L12: "     + nf(L12, 0, 0);

  outtxt += " , L23: "   + nf(L23, 0, 0);

  outtxt += " , L31: "   + nf(L31, 0, 0);

  outtxt += " , x3: "    + nf(x3,  0, 0);

  outtxt += " , y3: "    + nf(y3,  0, 0);

//  outtxt += " , A1: "    + nf(degrees(A1), 0, 1) + " deg ";

  outtxt += " , A2: "    + nf(degrees(A2), 0, 1) + " deg ";

//  outtxt += " , A3: "    + nf(degrees(A3), 0, 1) + " deg ";

//  outtxt += " , All: "    + nf(degrees(All), 0, 1) + " deg ";

  text(outtxt, 10, 14);

}

​

void link_info() {  // with processing IDE JAVA MODE links not work in console

  println(" org: https://editor.p5js.org/kll/sketches/rkRiXYYh7");

  println(" math: https://en.wikipedia.org/wiki/Circumscribed_circle");

  println(" wiki: https://en.wikipedia.org/wiki/Law_of_sines");

  println(" forum: https://discourse.processing.org/t/circumcircle-of-triangle/13030");

}

*/