Code archives/Networking/Cubic Spline Interpolation - Updated with Recursive Math

;-Cubic Spline Interpolation-;

;[Updated] - Recursive Math Added For fastest Spline Speed Ever

;-by Chroma
;-based on a tutorial at www.gamedev.net

;The object starts at position S and is predicted ahead one second to be at 1.
;The object is then predicted to E and then time reversed one second to 2.
;The spline is then plotted from S to E based on the predicted points of 1 and 2
;and the starting And ending velocities. The object is then moved along the
;spline Until the Next packet arrives and then process starts over.

;S = starting point - time=0
;1 = predicted position after 1 sec
;2 = predicted position reversed from E after 1 sec
;E = ending point

AppTitle "Cubic Spline Interpolation"

Graphics 350,250,16,2
SetBuffer BackBuffer()

;Main Loop
While Not KeyHit(1)
Cls

;Cubic Spline Interpolation (I love those words!)
cspline(50,180,100,50,300,75,-20,-10,0,0)

Flip
Wend
End

;-=-=-=-=-=-=-=-=-=-=-=-=-=-=;
;=Cubic Spline Interpolation=;
;-=-=-=-=-=-=-=-=-=-=-=-=-=-=;
Function cspline(Xold,Yold,Xvelold,Yvelold,XNew=0,YNew=0,Xvelnew,Yvelnew,XAccelNew,YAccelNew,Time=3)

;Init Local Variables
Local x,y,x0,y0,x1,y1,x2,y2,x3,y3
Local a,b,c,d,e,f,g,h,t#

;Coord#1 is the current object's X,Y (or X,Z if using 3D)
Color 0,255,0
X0=Xold : Y0=Yold
Text X0-4,Y0-16,"S"
Rect X0,Y0,3,3,1

;Calc Coord#2
Color 255,255,0
X1 = X0 + XVelOld
Y1 = Y0 + YVelOld
Text X1-4,Y1-16,"1"
Rect X1,Y1,3,3,1

;Calc Coord#3 (must calc after Coord#4)
Color 200,100,0
X2=XNew + XVelNew * Time + .5 * XAccelNew * Time^2
Y2=YNew + YVelNew * Time + .5 * YAccelNew * Time^2
Text X2-4,Y2-16,"2"
Rect X2,Y2,3,3,1

;Calc Coord#4
Color 255,0,0
X3=XNew
Y3=YNew
;X3=X2 - (XVelNew + XAccelNew * Time)
;Y3=Y2 - (YVelNew + YAccelNew * Time)
Text X3-4,Y3-16,"E"
Rect X3,Y3,3,3,1


;Calc Cubic Spline Points
RecursiveMathA=3*x2
RecursiveMathB=3*x1
RecursiveMathC=6*x1
RecursiveMathD=3*x0
RecursiveMathE=3*y2
RecursiveMathF=3*y1
RecursiveMathG=6*y1
RecursiveMathH=3*y0


A = X3 - RecursiveMathA + RecursiveMathB - x0
B = RecursiveMathA - RecursiveMathC + RecursiveMathD
C = RecursiveMathB - RecursiveMathD
D = x0
E = y3 - RecursiveMathE +RecursiveMathF - y0
F = RecursiveMathE - RecursiveMathG + RecursiveMathH
G = RecursiveMathF - RecursiveMathH
H = y0


;Draw the Spline
For t#=0 To 1 Step .001
	x = A*t^3 + B*t^2 + C*t + D
	y = E*t^3 + F*t^2 + G*t + H 
Plot x,y
Next

End Function