I introduced a Small Basic sample code about 2-dimensional vector in my last blog. A 2-D vector has two elements. A point in the plane has x coordinate and y coordinate. This kind of coordinate is called Cartesian coordinates.
Today, I'd like to introduce another coordinate system - polar coordinates. In polar coordinates, a point is represented with r (the length from the origin) and θ (the angle between the vector and the x axis). A sample program TJB764 shows both coordinates.
Conversion from polar coordinates to Cartesian coordinates
This is easy.
Small Basic code is as follows. A variable a means θ above.
x = r * Math.Cos(a)y = r * Math.Sin(a)Conversion from Cartesian coordinates to polar coodinates
This is basically easy.
Small Basic code is:
Sub Math_CartesianToPolar ' Math | convert Cartesian coodinate to polar coordinate ' param x, y - Cartesian coordinate ' return r, a - polar coordinate (0<=a<360) r = Math.SquareRoot(x * x + y * y) If x = 0 And y > 0 Then a = 90 ' [degree] ElseIf x = 0 And y < 0 Then a = -90 ElseIf x = 0 Then ' this condition is needed for SB 1.2 a = 0 Else a = Math.ArcTan(y / x) * 180 / Math.Pi EndIf If x < 0 Then a = a + 180 ElseIf x > 0 And y < 0 Then a = a + 360 EndIfEndSubI already wrote about this subroutine in this blog titled Small Basic Game Programming - Game Math. But the last one causes divide by zero error in Small Basic 1.2.
Math function tan-1 is Math.ArcTan() operation in Small Basic. The graph of this operation is:
