Cubic Bezier Curves

This code has been declared by its author to be Public Domain code.

Cubic Bezier Curves by ImaginaryHuman

2006

Just a simple program to let you rudimentally play with some cubic bezier curves. The actual bezier calculation is taken from code by Wedoe so I don't claim authorship of that part. This is generally OpenGL code, but doesn't have to be. There are 4 points per curve, since they are cubic. The distance from the first point to the second point acts as the tangent handle for the left half of the curve. The distance from the last point to the third point acts as the tangent handle for the right half of the curve.

'Cubic Bezier splines
'Adapted from code Wedoe

'Press Space for a totally new random spline
'Press left arrow to control the previous control point
'Press right arrow to control the next control point
'Press Escape to exit
'Move  mouse to see it adapt

Strict

Type Point
	Field x:Int
	Field y:Int
End Type
Const Accuracy:Double=0.03		'Lower has more line segments
	
SeedRnd(MilliSecs())	'Different each time
SetGraphicsDriver GLMax2DDriver()
Graphics 640,480,0
SetBlend LIGHTBLEND
Local DoAnother:Int
Local ControlPoint:Int
Local Counter:Int
glEnable(GL_LINE_SMOOTH)	'Quick antaliasing hack
glHint(GL_LINE_SMOOTH_HINT,GL_NICEST)
glLineWidth(3.0)
Repeat
	DoAnother=False
	Local NumPoints:Int=Rand(4,16)	'Whatever >3
	NumPoints=NumPoints-(NumPoints Mod 3)+1	'3 points per bezier plus 1, 4th point of each bez is shared
	Local Points:Point[NumPoints]
	For Local p:Int=0 To NumPoints-1
		Points[p]=New Point
		Points[p].x=Rand(20,620)
		Points[p].y=Rand(20,460)
	Next
	ControlPoint=NumPoints/2
	Repeat
		Cls
		Points[ControlPoint].x=MouseX()
		Points[ControlPoint].y=MouseY()
		'Draw controls
		For Local p:Int=0 To NumPoints-1
			SetColor $88,$88,$88
			DrawLine Points[p].x-7,Points[p].y-7,Points[p].x+7,Points[p].y+7
			DrawLine Points[p].x-7,Points[p].y+7,Points[p].x+7,Points[p].y-7
			SetColor $00,$44,$88
			DrawLine Points[p].x,Points[p].y,Points[Min(NumPoints-1,p+1)].x,Points[Min(NumPoints-1,p+1)].y
			DrawText p,Points[p].x+5,Points[p].y+5
		Next
		'Draw segments
		Local PrevX:Double,PrevY:Double
		SetColor $FF,$FF,$FF
		Counter=0
		For Local S:Int=0 To NumPoints-4 Step 3
			For Local T:Double=0 To 1 Step Accuracy
				Local X:Double=Points[s].x*(1-T)^3 + 3*Points[s+1].x*(1-T)^2*T + 3*Points[s+2].x*(1-T)*T^2 + Points[s+3].x*T^3
				Local Y:Double=Points[s].y*(1-T)^3 + 3*Points[s+1].y*(1-T)^2*T + 3*Points[s+2].y*(1-T)*T^2 + Points[s+3].y*T^3
				If PrevX=0 And PrevY=0
					PrevX=X
					PrevY=Y
				EndIf
				DrawLine PrevX,PrevY,X,Y,False
				PrevX=X
				PrevY=Y
				Counter:+1
			Next
		Next
		DrawLine PrevX,PrevY,Points[NumPoints-1].x,Points[NumPoints-1].y
		DrawText "Edges: "+String(Counter),0,10
		DrawText "Controls: "+String(NumPoints),0,20
		DrawText "Curves: "+String(NumPoints/3),0,30
		Flip
		If KeyHit(KEY_SPACE) Then DoAnother=True
		If KeyHit(KEY_LEFT) Then ControlPoint=Max(0,ControlPoint-1)
		If KeyHit(KEY_RIGHT) Then ControlPoint=Min(NumPoints-1,ControlPoint+1)
	Until KeyHit(KEY_ESCAPE) Or DoAnother=True
Until DoAnother=False

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