B4J Tutorial See whether (and where) circles intersect

Using B4XCanvas and DrawCircle, and geometry laws, we can test whether two given circles intersect or not.
If they intersect the points of intersections are returned.

Circle Equations​

Assuming two circles with:

The intersection points (if they exist) can be calculated as follows:

1. Calculate Distance Between Circle Centers:
   
   
2. Check for Intersection:
   • 
3. Calculate Intersection Points:
   • Calculate a and h, which determine the position of the intersection points.
   • 
   • Determine the points P2 as the base point on the line between the centers of the circles:
   • 
   • Find the offset points to get the intersection points:
   • 

Translate this into b4j:

Sub FindIntersectionPoints(x1 As Double, y1 As Double, r1 As Double, x2 As Double, y2 As Double, r2 As Double) As List
    Dim result As List
    result.Initialize
 
    Dim d As Double = Sqrt(Power(x2 - x1, 2) + Power(y2 - y1, 2))
 
    ' Check if circles intersect
    If d > r1 + r2 Or d < Abs(r1 - r2) Then
        Log("No intersection points.")
        Return result
    End If

    ' Calculate a and h
    Dim a As Double = (Power(r1, 2) - Power(r2, 2) + Power(d, 2)) / (2 * d)
    Dim h As Double = Sqrt(Power(r1, 2) - Power(a, 2))
 
    ' Calculate the base point on the line between the circles' centers
    Dim x3 As Double = x1 + a * (x2 - x1) / d
    Dim y3 As Double = y1 + a * (y2 - y1) / d
 
    ' Calculate the two intersection points
    Dim x4_1 As Double = x3 + h * (y2 - y1) / d
    Dim y4_1 As Double = y3 - h * (x2 - x1) / d
 
    Dim x4_2 As Double = x3 - h * (y2 - y1) / d
    Dim y4_2 As Double = y3 + h * (x2 - x1) / d
 
    ' Add the points to the result list
    result.Add(CreateMap("x" : x4_1, "y" : y4_1))
    result.Add(CreateMap("x" : x4_2, "y" : y4_2))
 
    Return result
End Sub

You can call this function and then draw the intersection points on the canvas:

Sub DrawIntersections
    Dim x1 As Double = 100, y1 As Double = 100, r1 As Double = 75
    Dim x2 As Double = 150, y2 As Double = 100, r2 As Double = 75
    Dim intersections As List = FindIntersectionPoints(x1, y1, r1, x2, y2, r2)
 
    Dim cvs As B4XCanvas
    cvs.Initialize(mainForm.rootPane)
    cvs.DrawCircle(x1, y1, r1, xui.Color_Blue, False, 2dip)
    cvs.DrawCircle(x2, y2, r2, xui.Color_Red, False, 2dip)
 
    For Each p As Map In intersections
        Dim px As Double = p.Get("x")
        Dim py As Double = p.Get("y")
        cvs.DrawCircle(px, py, 5dip, xui.Color_Green, True, 1dip)
    Next
 
    cvs.Refresh
End Sub

 

[TILogistic]

A tutorial to understand collision detection

Collision Detection and Physics - JavaScript Tutorial | Spicy Yoghurt

Perform collision detection and react with physics, using JavaScript. Check for overlap between shapes, apply hitboxes and calculate new velocities. Make it more natural with object mass, gravity and restitution. By the end of this tutorial, you'll have a basic physics simulation running in your...

spicyyoghurt.com