Submission

Submission deadline: 11:59 pm, Sunday, September 15 2024.

Submission method: Run the included submit.py script in your root exercise repository. You will need Python and Requests installed. If you do not have Python and/or Requests, you can either:

• Install Python and/or Requests
• Copy your assignment solution (the exercises folder) and the submit script to rlogin and run the submit script there

  # Example:
  $ scp -r exercises/ submit.py \
    <VT_USERNAME_HERE>@rlogin.cs.vt.edu:cs3984-exercise-1
  
  
  

Details

1. The shapes live in an infinite grid with the following coordinate system:

   • The x-coordinate increases from left to right.
   • The y-coordinate increases from top to bottom.

2. A Circle can be created from its center and radius.

3. A Rectangle can be created from

   • the top-left corner (the corner of the rectangle with the smallest x and y coordinate), a width (in the positive x direction), and a height (in the positive y direction)

   • any two diagonally opposing corners

4. A Rectangle should provide the following information:

   • x_min: the smallest x-coordinate located within the rectangle (or the x-coordinate of the left edge of the rectangle)
   • x_max: the largest x-coordinate located within the rectangle (or the x-coordinate of the right edge of the rectangle)
   • y_min: the smallest y-coordinate located within the rectangle (or the y-coordinate of the top edge of the rectangle)
   • y_max: the largest y-coordinate located within the rectangle (or the y-coordinate of the bottom edge of the rectangle)

Formulas

Circle-circle intersection formula for circles $A$ and $B$: $$\begin{align*} \text{radiiSumSq}_{AB} &= (A_{radius} + B_{radius})^2\\ \text{centerDiff}_{AB} &= (A_{cx} - B_{cx})^2 + (A_{cy} - B_{cy})^2\\ \text{Overlap}_{AB} &= (\text{centerDiff}_{AB} \le \text{radiiSumSq}_{AB}) \end{align*}$$

Rectangle-rectangle intersection formula for rectangles $A$ and $B$: $$\begin{align*} \text{xOverlap}_{AB} &= (A_{x\_min} \lt B_{x\_max}) \land (A_{x\_max} \gt B_{x\_min})\\ \text{yOverlap}_{AB} &= (A_{y\_max} \gt B_{y\_min}) \land (A_{y\_min} \lt B_{y\_max})\\ \text{Overlap}_{AB} &= \text{xOverlap}_{AB} \land \text{yOverlap}_{AB} \end{align*}$$

Circle-rectangle intersection formula for circle $C$ and rectangle $R$: $$\begin{align*} \text{closestX}_{CR} &= \text{clamp}(C_{cx}, R_{x\_min}, R_{x\_max})\\ \text{closestY}_{CR} &= \text{clamp}(C_{cy}, R_{y\_min}, R_{y\_max})\\ \text{distanceX}_{CR} &= C_{cx} - \text{closestX}_{CR}\\ \text{distanceY}_{CR} &= C_{cy} - \text{closestY}_{CR}\\ \text{distanceSq}_{CR} &= {\text{distanceX}_{CR}}^2 + {\text{distanceY}_{CR}}^2\\ \text{circleRadiusSq}_{CR} &= {C_{radius}}^2\\ \text{Overlap}_{CR} &= \text{distanceSq} \lt \text{circleRadiusSq} \end{align*}$$

Note: $\text{clamp}(x, a, b) = \text{max}(a, \text{min}(x, b))$

Interactive Demo