How to get bounding-box of different Shapes in p5.js ?

In this article, we will see how to get the bounding-box of different shapes. We will use P5.js which is a Javascript framework creative programming environment and is very much inspired by Processing.

Bounding-box: A bounding-box is basically just a rectangle that bounds a shape more technically it is the rectangle with the smallest possible surface area that bounds the shape. A bounding-box can have rotation (called global bounding-box) but in this article, we’ll be focusing around the axis-aligned bounding boxes (AABB shapes) which have zero rotation in them (also called local bounding-box)

Note: A Bounding-Box for a shape is the rectangle with the smallest possible surface area that bounds the shape.

Reason to calculate bounding-box: A bounding-box acts as a container of a shape and has several applications in graphical applications (most notably used by GUI libraries for widget-masks). Since a bounding-box contains the shape so if any other shape doesn’t intersect with the bounding-box then it also doesn’t intersect with the inner-shape thus bounding-boxes are used heavily in Physics engines (such as Box2D) for broad-phase collision detection.

Base for the p5.js: This is the base-code (normally for every p5.js code).

Note: We will only change script.js at every iteration, and the HTML file will necessarily remain intact!

• Finding bounding-box of an ellipse:

  
  

  
  
  

  /* p5.js Sketch for finding and drawing    bounding-box of an ellipse*/ function setup(){   createCanvas(480, 360); }    // Draws bounding-box around the // given ellipse! function drawBBox(x0, y0, r1, r2){      // Draw only the outline   // of the rectangle   noFill();      // Draw the outline in red   stroke(255, 0, 0);   rect(x0-r1, y0-r2, 2*r1, 2*r2); } function draw() {   let x0 = width/2, y0 = height/2;   let r1 = 180, r2 = 100;      // Note that `ellipse` takes in   // diameters not radii!   ellipse(x0, y0, 2*r1, 2*r2);   drawBBox(x0, y0, r1, r2);      // We don't want to draw this   // over and over again   noLoop(); }

  Output:
  

• Finding bounding-box of a circle: It is same as an ellipse, since a circle is just a special case of an ellipse with same radii (same semi-major-axis and semi-minor axis).
• Finding bounding-box of a line-segment

  
  

  
  
  

  /* p5.js Sketch for finding and drawing   bounding-box of a line-segment*/ function setup() {   createCanvas(480, 360); }    // Draws bounding-box around the // given line-segment! function drawBBox(x1, y1, x2, y2) {   stroke(255, 0, 0);   noFill();   let x = min(x1, x2), y = min(y1, y2);   let w = max(x1, x2) - x, h = max(y1, y2) - y;   rect(x, y, w, h); }    function draw() {   let x1 = 280, y1 = 80, x2 = 180, y2 = 280;   line(x1, y1, x2, y2);   drawBBox(x1, y1, x2, y2);   noLoop(); }

  Output:
  

• Finding bounding-box of a triangle: Finding bounding-box of a triangle is very similar to finding bounding-box for line-segment.

  
  

  
  
  

  /* p5.js Sketch for finding and drawing   bounding-box of a triangle*/ function setup() {   createCanvas(480, 360); }    // Draws bounding-box around the // given triangle! function drawBBox(x1, y1, x2, y2, x3, y3) {   stroke(255, 0, 0);   noFill();   let x = min(x1, x2, x3), y = min(y1, y2, y3);   let w = max(x1, x2, x3) - x, h = max(y1, y2, y3) - y;   rect(x, y, w, h); }    function draw() {   let x1 = 240, y1 = 80, x2 = 140;   let y2 = 280, x3 = 340, y3 = 280;      triangle(x1, y1, x2, y2, x3, y3);   drawBBox(x1, y1, x2, y2, x3, y3);   noLoop(); }

  Output:
  

• Finding bounding-box of a polygon: A triangle is a polygon, and if we find the bounding-box of a triangle then finding bounding-box for polygon shouldn’t be any difficulty. We just have to generalize so that we can have any number of vertices and we are done.

  
  

  
  
  

  /* p5.js sketch for finding and drawing   bounding-box of a polygon*/ function setup() {   createCanvas(480, 360); }    // Draws bounding-box around // the given polygon! function drawBBox(x, y) {   stroke(255, 0, 0);   noFill();   let rx = min(x), ry = min(y);   let w = max(x) - rx, h = max(y) - ry;   rect(rx, ry, w, h); }    function draw(){   /* Vertices for a star-polygon (decagon) */   let x = [240, 268, 334, 286, 298,            240, 182, 194, 146, 212];   let y = [80, 140, 150, 194, 260,            230, 260, 194, 150, 140];      beginShape();      for (let i = 0; i < x.length; ++i)     vertex(x[i], y[i]);   fill(255, 217, 0);      // If you don't CLOSE it then it'd   // draw a chained line-segment   endShape(CLOSE);   drawBBox(x, y);   noLoop(); }

  Output:
  

Finding Bounding-Boxes is an important part of visualization applications. Also in dynamic applications such as games, one cannot compute capsule-collision detection at every frame without entailing a punishment in the performance. So before any complex collision-checking, a broad-phase check is made for early exit which returns false as soon as it is ascertained that the shape doesn’t collide with the other shape. If the broad-phase check is passed then comes the narrow-phase where the actual collision-detection (OOBB, SAT, capsule, ellipsoid, etc) happens! Hence finding the bounding-box is an important part of many graphics-rich applications for various reasons.