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

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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).

<!-- Our main HTML file! -->
<html> 
  <head> 
    <script src="https://cdn.jsdelivr.net/npm/p5"></script> 
    <script src="sketch.js"></script> 
  </head> 
  <body> 
  </body> 
</html> 

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.

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