;Simple spline interpolation - get Y from X
;(x0,y0),(x1,y1),(x2,y2),(x3,y3) = 4 known sequential points in increasing x order
;x = x coordinate we wish to interpolate for (must satisfy (x1 <= x < x2)
Function SplineY#(x0#, y0#, x1#, y1#, x2#, y2#, x3#, y3#, x#)
;known gradients:
a1# = (y2-y0) / (x2-x0)
a2# = (y3-y1) / (x3-x1)
;Linear equations for points 1 and 2:
c1# = y1 - a1 * x1
c2# = y2 - a2 * x2
;Interpolate to get equation at point (x,y):
t# = (x - x1) / (x2 - x1)
t# = (Cos(180 * (1 - t)) + 1) / 2 ;(This smooths the transition using cos)
c# = c1 * (1 - t) + c2 * t
a# = a1 * (1 - t) + a2 * t
Return a * x + c
End Function
Function SplineYGradient#(x0#, y0#, x1#, y1#, x2#, y2#, x3#, y3#, x#)
;known gradients:
a1# = (y2-y0) / (x2-x0)
a2# = (y3-y1) / (x3-x1)
;Interpolate to get equation at point (x,y):
t# = (x - x1) / (x2 - x1)
t# = (Cos(180 * (1 - t)) + 1) / 2 ;(This smooths the transition using cos)
a# = a1 * (1 - t) + a2 * t
Return a
End Function
Example
Function Example()
Local yvalues#[6]
yvalues[0] = Rnd(600)
yvalues[1] = Rnd(600)
yvalues[2] = Rnd(600)
yvalues[3] = Rnd(600)
yvalues[4] = Rnd(600)
yvalues[5] = Rnd(600)
yvalues[6] = Rnd(600)
Graphics 800, 600
SetBuffer BackBuffer()
Cls
Color 255,0,0
For x# = 0 To 5 Step 1
Oval x*100+100-2, yvalues[x]-2, 4, 4, False
Next
Color 255,255,255
For x# = 1.0 To 5 Step 0.01
x0# = Floor(x) -1
x1# = Floor(x)
x2# = Floor(x) +1
x3# = Floor(x) +2
y0# = yvalues[x0-1]
y1# = yvalues[x0]
y2# = yvalues[x0+1]
y3# = yvalues[x0+2]
y# = SplineY(x0, y0, x1, y1, x2, y2, x3, y3, x)
Plot x*100, y
Next
Flip
WaitKey
End Function |
