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Code archives/Algorithms/Cubic spline interpolation

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

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Cubic spline interpolation by Matt Merkulov(Posted 1+ years ago)
From article: Cubic spline interpolation (rus)
;Drawing cubic spline function graph what is passing thru random set of points by Matt Merkulov

SeedRnd MilliSecs ()

Dim ptx#(81)
Dim pty#(81)

Graphics 800,600

; The circuit from points is created
x#=0
y#=300
Color 255,0,0
Repeat
 q=q+1
 ptx#(q)=x#
 pty#(q)=y#
 Oval x#-4, y#-4,9,9
 x#=x#+ Rnd (30,100)
 y#=y#+ Rnd (-100,100)
Until x#>=800

Color 255,255,255
; A cycle on all pieces (for an extreme right point of a piece is not present)
For n=1 To q-1
 d#=pty#(n)
 If n=1 Then
 ; If the initial piece the derivative is equal 0 (since an adjacent point undertakes
 ; At the left, necessary for definition of factor is absent
 c#=0
 Else
 ; Calculation of the factor equal to derivative N1 under the formula
 c#=(pty#(n+1)-pty#(n-1)) / (ptx#(n+1)-ptx#(n-1))
 End If
 ; Derivative N2 is similarly calculated
 If n=q Then
 dy2#=0
 Else
 dy2#=(pty#(n+2)-pty#(n)) / (ptx#(n+2)-ptx#(n))
 End If
 ; Calculation of other factors of a multinominal
 x3#=ptx#(n+1)-ptx#(n)
 xx3#=x3#*x3#
 b#=(3*pty#(n+1)-dy2#*x3#-2*c#*x3#-3*d#)/xx3#
 a#=(dy2#-2*b#*x3#-c#) / (3*xx3#)
 ; Construction of a piece of a curve
 For x#=0 To x3#
 xx#=x#*x#
 y#=a#*xx#*x#+ b#*xx#+ c#*x#+ d#
 x1#=x#+ ptx#(n)  
 If x1#> 0 Then
  y1#=y#
  If y1#<-3 Then y1#=-3 ElseIf y1#> 602 Then y1#=602
  If y2#<-3 Then y2#=-3 ElseIf y2#> 602 Then y2#=602
  If y2#<y1#Then z#=y1#:y1#=y2#:y2#=z#
  For yy#=y1#To y2#
  Rect x1#-1, yy#-1,3,3
  Next
 End If
 y2#=y#
 Next
Next
WaitKey

Comments

TAS(Posted 1+ years ago)
Nice, need to insert a flip comand before the Waitkey to see the results in BlitzPlus


TAS(Posted 1+ years ago)
;TAS 12-6-08
;mostly for my oun use I
;added some clarifing comments
;and polish the graphics somewhat


;ID: 1953
;Author: Matt Merkulov
;Date: 2007-03-14 11:06:27
;Title: Cubic spline interpolation
;Description: Drawing cubic spline what is passing thru random set of points
;Drawing cubic spline function graph what is passing thru random set of points by Matt Merkulov
;Inessecene; draws a curve through two points based on a 3rd order equation
;that's fitted to four points (e.g. the two points plus the preceeding and following point)


Dim ptx#(8),pty#(8)

Graphics 800,600
SetBuffer BackBuffer()

;Create route of random points
Color 255,0,0
q=5
For i=1 To q
Read ptx(i),pty(i)
Oval ptx(i)-4,pty(i)-4,9,9
Text ptx(i)-4,pty(i)-16,i
Next
Color 255,255,255
t0=MilliSecs()

For n=1 To q-1 ;q number of data points
y0#=pty(n)
;These factors are effected by points n-1 and n+2
If n=1 Then c#=0 Else c#=(pty#(n+1)-pty#(n-1)) / (ptx#(n+1)- ptx#(n-1) )
If n=q Then dy2#=0 Else dy2#=(pty#(n+2)-pty#(n)) / (ptx#(n+2)-ptx#(n))

;Calculate factors of the multinominal
dx%=ptx(n+1)-ptx(n)
c3%=dx*dx
b#=(3*pty(n+1)-dy2#*dx-2*c#*dx-3*y0)/c3
a#=(dy2#-2*b#*dx-c#) / (3*c3)

;calculate hypothnuse distance
dy%=pty(n+1)-pty(n)
r#=Sqr(dx*dx+dy*dy)

;Draw the curve from point n to n+1
;by calculating x and y while traveling along r
For dr%=0 To r
x#=(dx*dr)/r# ;needs to be a real number due to possibllity of dy>>dx
;use the fitted 3rd order equation to calculate y from x
y%=a#*(x*x*x) + b#*(x*x) + c#*(x) + y0
Rect ptx(n)+x-1,y-1,3,3
Next
Next

Text 100,300,MilliSecs()-t0
Text 100,320,"Any Key"

Flip
WaitKey
End


Data 100,100
Data 200,200
Data 300,150
Data 400,50
Data 500,300


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