# Interpolate a path with equal steps

// Interpolate to create a path with equal spacing between successive points in the XY plane.
// the path described by xwave and ywave as inputs needs to be quite smooth for this to work.
// play with step size (step), number of nodes for interpolation (numNodes) and linear vs. cubic spline
// interpolation (flagT = 1, 2) to optimise the path output as xout and yout.
// step size must be rather small with respect to spacing of path points in xwave, ywave

function StepInterpolate(xwave, ywave, step, flagT, numNodes)
wave xwave, ywave
variable step, flagT, numNodes

make /o/n=1 xout, yout
xout=xwave[0]
yout=ywave[0]

make /o/n=(numNodes) w_nodesX, w_nodesY
make /o/n=200 w_interp

variable inPnt=0, outPnt=0, minPnt
variable nextX, nextY

variable i, inc=(wavemax(xwave)-wavemin(xwave))/1e5

do
minPnt=ceil(inPnt-numNodes/2)
minPnt=max(0, Minpnt)
minPnt=min(minPnt, numpnts(xwave)-numNodes)

w_nodesX=xwave[minPnt+p]
w_nodesY=ywave[minPnt+p]

if ( (wavemax(w_nodesY)-wavemin(w_nodesY)) < (wavemax(w_nodesX)-wavemin(w_nodesX)) )
// heading in a 'horizontal' direction

Interpolate2/T=(flagT)/N=200/E=2/Y=w_interp w_nodesX, w_nodesY

nextX=xout[outPnt]
i=0
do
i+=1
if (i>1e5)
return 0
endif
nextX+=inc*sign(w_nodesX[numpnts(w_nodesX)-1]-w_nodesX[0])
while (sqrt( (w_interp(nextX)-yout[outPnt])^2 + (nextX-xout[outPnt])^2 ) < step )
nextY=w_interp(nextX)
if (nextX<min(xwave[inPnt], xwave[inpnt+1]) || nextX>max(xwave[inPnt], xwave[inpnt+1]) )
do
inPnt+=1
if(inPnt>(numpnts(ywave)-1))
return 1
endif
while ( (nextX<min(xwave[inPnt], xwave[inpnt+1])) || (nextX>max(xwave[inPnt], xwave[inpnt+1])) )
endif

else // heading in a "more vertical" direction

Interpolate2/T=(flagT)/N=200/E=2/Y=w_interp w_nodesY, w_nodesX

nextY=Yout[outPnt]
i=0
do
i+=1
if (i>1e5)
return 0
endif
nextY+=inc*sign(w_nodesY[numpnts(w_nodesY)-1]-w_nodesY[0])
while (sqrt( (nextY-yout[outPnt])^2 + (w_interp(nextY)-xout[outPnt])^2 ) < step )
nextX=w_interp(nextY)

if (nextY<min(ywave[inPnt], ywave[inpnt+1]) || nextY>max(ywave[inPnt], ywave[inpnt+1]) )
do
inPnt+=1
if(inPnt>(numpnts(ywave)-1) )
return 2
endif
while (nextY<min(ywave[inPnt], ywave[inpnt+1]) || nextY>max(ywave[inPnt], ywave[inpnt+1]) )
endif
endif

outPnt+=1
insertpoints outPnt, 1, xout, yout
xout[outpnt]=nextX
yout[outpnt]=nextY

while(inPnt<numpnts(xwave))
return 3
end

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