Code archives/Algorithms/Cubic spline interpolation

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

Download source code

Cubic spline interpolation by Matt Merkulov
(Posted 20 years ago)
From article: Cubic spline interpolation (rus)
Open in online IDE
;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 18 years ago)
Nice, need to insert a flip comand before the Waitkey to see the results in BlitzPlus

TAS
(Posted 18 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

Code Archives Forum