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"Bezier Curve Functions"
, by world_creator
Creates bezier curves of course.
Code
; // Initialize Graphics! Graphics 640,480,32,0 SeedRnd MilliSecs() ; // Initialize Control Points for 4 point bezier x1#=Rand(100,540) y1#=Rand(100,380) x2#=Rand(100,540) y2#=Rand(100,380) x3#=Rand(100,540) y3#=Rand(100,380) x4#=Rand(100,540) y4#=Rand(100,380) ; // Initialize Control Points for 3 point bezier a1#=Rand(100,540) b1#=Rand(100,380) a2#=Rand(100,540) b2#=Rand(100,380) a3#=Rand(100,540) b3#=Rand(100,380) ; // Initialize buffer for drawing SetBuffer BackBuffer() ; // Don't worry about this, these are variables for the control point selection and misc md=False mdid=0 size=0 detail=3 detailinc#=0 drawmode=0 ; // This is just a font. verdana12=LoadFont("Verdana",12,False,False,False) ; // Start loop! Exit when escape key is pressed. While Not KeyDown(1) ; // Clear screen! Cls ; // Check for control point selection, don't worry about this little doozy. Gosub control_point_selection ; // Print instructions! Color 255,255,255 SetFont verdana12 Text 0,(12*0),"Bezier Functions (3 and 4 Control Points)" Text 0,(12*1),"by Jonathan Nguyen" Text 0,(12*2),"jnguyen327@gmail.com" Text 0,(12*4),"Drag control points to manipulate bezier" Text 0,(12*5),"Space: Toggle line drawing." Text 0,(12*6),"-/+: Change detail of curve" If drawmode=0 Text 0,(12*8),"Current Draw Mode: Dots" Else Text 0,(12*8),"Current Draw Mode: Line" EndIf Text 0,(12*9),"Current Detail Level: "+Str$(detail) ; // User controls If KeyHit(57)=True Then drawmode=drawmode+1 If drawmode=2 Then drawmode=0 If KeyHit(12)=True Then detail=detail-1 If KeyHit(13)=True Then detail=detail+1 If detail<1 Then detail=1 If detail>6 Then detail=6 Select detail Case 1 detailinc#=0.1 Case 2 detailinc#=0.05 Case 3 detailinc#=0.01 Case 4 detailinc#=0.005 Case 5 detailinc#=0.001 Case 6 detailinc#=0.0005 End Select ; // Prep for drawing 4 point bezier Color 255,255,128 If drawmode=0 t#=0 endt#=1 Else t#=detailinc# endt#=1+detailinc# EndIf ; // Start loop to cycle through t# values (distance along curve) Repeat ; // Call functions to retrieve bezier curve coordinates. x#=Bezier4X#(t#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#) y#=Bezier4Y#(t#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#) ; // Draw the curve based on draw mode. If drawmode=0 Plot x#,y# Else Line x#,y#,Bezier4X#(t#-detailinc#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#),Bezier4Y#(t#-detailinc#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#) EndIf ; // Increment the t# value t#=t#+detailinc# ; // End that loop Until t#=>endt# ; // Prep for drawing 3 point bezier Color 128,255,255 If drawmode=0 t#=0 endt#=1 Else t#=detailinc# endt#=1+detailinc# EndIf ; // Start loop to cycle through t# values (distance along curve) Repeat ; // Call functions to retrieve bezier curve coordinates. x#=Bezier3X#(t#,a1#,b1#,a2#,b2#,a3#,b3#) y#=Bezier3Y#(t#,a1#,b1#,a2#,b2#,a3#,b3#) ; // Draw the curve based on draw mode. If drawmode=0 Plot x#,y# Else Line x#,y#,Bezier3X#(t#-detailinc#,a1#,b1#,a2#,b2#,a3#,b3#),Bezier3Y#(t#-detailinc#,a1#,b1#,a2#,b2#,a3#,b3#) EndIf ; // Increment the t# value t#=t#+detailinc# ; // End that loop Until t#=>endt# ; // Draw Cursor Line MouseX()-4,MouseY(),MouseX()+4,MouseY() Line MouseX(),MouseY()-4,MouseX(),MouseY()+4 ; // Flip Back and Front Buffers Flip False ; // End loop! Wend End ; //////////////////////////////////////////////////////// ; // Bezier Functions ; How it works is you enter the control points and the time ; and it'll give you the coordinate along the curve based ; on the time. How the time works is that at 0 it's at the ; beginning point and at 1 at the end point. So basically, ; the middle point is when t#=0.5. One of the neat things ; about this is that if you just increase the function by ; one dimension then you can create 3d bezier curves. ; // 4 Point ; The parameters for this one: ; t# = distance along curve (0.0 To 1.0) ; (x1#,y1#) = Coordinates for start point ; (x2#,y2#) = Coordinates for first control point ; (x3#,y3#) = Coordinates for second control point ; (x4#,y4#) = Coordinates for end point ; // X Coordinate Function Function Bezier4X#(t#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#) Return x1#*(1-t#)^3 + 3*x2#*t#*(1-t#)^2 + 3*x3#*t#^2*(1-t#) + x4#*t#^3 End Function ; // Y Coordinate Function Function Bezier4Y#(t#,x1#,y1#,x2#,y2#,x3#,y3#,x4#,y4#) Return y1#*(1-t#)^3 + 3*y2#*t#*(1-t#)^2 + 3*y3#*t#^2*(1-t#) + y4#*t#^3 End Function ; // 3 Point ; The only difference in this one is that the two control ; points are merged into one if you don't need two. Yes, you ; could have done it on your own but knowing programmers you ; probably would have been too lazy to ;). ; The parameters for this one: ; t# = distance along curve (0.0 To 1.0) ; (x1#,y1#) = Coordinates for start point ; (x2#,y2#) = Coordinates for first control point ; (x3#,y3#) = Coordinates for end point ; // X Coordinate Function Function Bezier3X#(t#,x1#,y1#,x2#,y2#,x3#,y3#) Return x1#*(1-t#)^3 + 3*x2#*t#*(1-t#)^2 + 3*x2#*t#^2*(1-t#) + x3#*t#^3 End Function ; // Y Coordinate Function Function Bezier3Y#(t#,x1#,y1#,x2#,y2#,x3#,y3#) Return y1#*(1-t#)^3 + 3*y2#*t#*(1-t#)^2 + 3*y2#*t#^2*(1-t#) + y3#*t#^3 End Function ; //////////////////////////////////////////////////////// ; // Don't worry about any of this, this is just the control point selection code. .control_point_selection Color 128,128,128 Line x1#,y1#,x2#,y2# Line x2#,y2#,x3#,y3# Line x3#,y3#,x4#,y4# Line a1#,b1#,a2#,b2# Line a2#,b2#,a3#,b3# If md=True And mdid=1 x1#=MouseX() y1#=MouseY() Color 255,0,0 size=4 Else If mouseover(x1#-2,y1#-2,x1#+2,y1#+2)=True Color 0,255,0 size=4 Else Color 255,255,0 size=2 EndIf EndIf Oval x1#-size,y1#-size,size*2+1,size*2+1 If md=True And mdid=2 x2#=MouseX() y2#=MouseY() Color 255,0,0 size=4 Else If mouseover(x2#-2,y2#-2,x2#+2,y2#+2)=True Color 0,255,0 size=4 Else Color 255,255,0 size=2 EndIf EndIf Oval x2#-size,y2#-size,size*2+1,size*2+1 If md=True And mdid=3 x3#=MouseX() y3#=MouseY() Color 255,0,0 size=4 Else If mouseover(x3#-2,y3#-2,x3#+2,y3#+2)=True Color 0,255,0 size=4 Else Color 255,255,0 size=2 EndIf EndIf Oval x3#-size,y3#-size,size*2+1,size*2+1 If md=True And mdid=4 x4#=MouseX() y4#=MouseY() Color 255,0,0 size=4 Else If mouseover(x4#-2,y4#-2,x4#+2,y4#+2)=True Color 0,255,0 size=4 Else Color 255,255,0 size=2 EndIf EndIf Oval x4#-size,y4#-size,size*2+1,size*2+1 If md=True And mdid=5 a1#=MouseX() b1#=MouseY() Color 255,0,0 size=4 Else If mouseover(a1#-2,b1#-2,a1#+2,b1#+2)=True Color 0,0,255 size=4 Else Color 0,255,255 size=2 EndIf EndIf Rect a1#-size,b1#-size,size*2+1,size*2+1 If md=True And mdid=6 a2#=MouseX() b2#=MouseY() Color 255,0,0 size=4 Else If mouseover(a2#-2,b2#-2,a2#+2,b2#+2)=True Color 0,0,255 size=4 Else Color 0,255,255 size=2 EndIf EndIf Rect a2#-size,b2#-size,size*2+1,size*2+1 If md=True And mdid=7 a3#=MouseX() b3#=MouseY() Color 255,0,0 size=4 Else If mouseover(a3#-2,b3#-2,a3#+2,b3#+2)=True Color 0,0,255 size=4 Else Color 0,255,255 size=2 EndIf EndIf Rect a3#-size,b3#-size,size*2+1,size*2+1 If mouseover(x1#-2,y1#-2,x1#+2,y1#+2)=True If md=True mdid=1 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(x2#-2,y2#-2,x2#+2,y2#+2)=True If md=True mdid=2 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(x3#-2,y3#-2,x3#+2,y3#+2)=True If md=True mdid=3 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(x4#-2,y4#-2,x4#+2,y4#+2)=True If md=True mdid=4 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(a1#-2,b1#-2,a1#+2,b1#+2)=True If md=True mdid=5 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(a2#-2,b2#-2,a2#+2,b2#+2)=True If md=True mdid=6 Else If MouseDown(1)=True Then md=True EndIf EndIf If mouseover(a3#-2,b3#-2,a3#+2,b3#+2)=True If md=True mdid=7 Else If MouseDown(1)=True Then md=True EndIf EndIf If MouseDown(1)=False And md=True md=False mdid=0 EndIf Color 255,255,0 Text x1#+8,y1#,"4p,Start",False,True Text x2#+8,y2#,"4p,CP 1",False,True Text x3#+8,y3#,"4p,CP 2",False,True Text x4#+8,y4#,"4p,End",False,True Color 0,255,255 Text a1#+8,b1#,"3p,Start",False,True Text a2#+8,b2#,"3p,CP",False,True Text a3#+8,b3#,"3p,End",False,True Return ; // The end of that needlessly long control point selection code! ; // This is just a small mouse over check function I whipped up. Function mouseover(x1,y1,x2,y2) If MouseX()>x1 And MouseX()<x2 If MouseY()>y1 And MouseY()<y2 Return True Else Return False EndIf Else Return False EndIf End Function
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