find closest point on a curve to a fixed point in space

[s...@weacceptyou.com]

Hello there,

i have a point in space and a nearby curve that is running close to the point but not touching. Is there a special python/pymel way of finding the closest point on the curve to this point in space?

any tips welcome,

thanks,
Sam

[Sasha C]

Hi Sam,

I had a similar problem, but from point to a line segment which is straight. Look at this code, may be it can be of help:



def closestPointOnLineSegment(lineStartPoint, lineEndPoint, pointInSpace, ignoreNoProjections=True):
    '''
    Find a closest point on the line segment (defined by 2 points) to a given point in space.
    NOTE: There may be more limitations - be aware when using!
    Based on "Using Vector Mathematic, Finding closest point on a line", http://nic-gamedev.blogspot.dk/2011/11/using-vector-mathematics-and-bit-of_08.html
    #---parameters---------------------------------------
    # lineStartPoint       # float list     # A list of 3 elements to represent a point, that defines the start of the line segment.
    # lineEndPoint         # float list     # A list of 3 elements to represent a point, that defines the end of the line segment.
    # pointInSpace         # float list     # A list of 3 elements to represent a point in space.
    # ignoreNoProjections  # boolean        # Points in space that have no perpendicular to the given line segment will be ignored.
    #---return-------------------------------------------
    #                      # float list     # A list of 3 elements to represent a point between line points, that is closest to the given point in space.
    #                                       # If ignoreNoProjections=True and point is outside the segment - will return a zero vector [0.0, 0.0, 0.0]
    #---example------------------------------------------
    # closestPointOnLineSegment(lineStartPoint=[61.87, 4.31, 1.85], lineEndPoint=[65.97, 4.15, 2.37], pointInSpace=[67.89, 3.71, 2.60])
    #----------------------------------------------------
    author      Alexandra "Sasha" Ciolac
    version     1.1
    last update 07.03.2013
    #---Update log---------------------------------------
   '''  
    ac = vecSubtract(vectorA=lineEndPoint, vectorB=lineStartPoint) # Find vector between start and end of the line
    l2 = vecMag(vector=ac) * vecMag(vector=ac) # Find it's square length
    ba = vecSubtract(vectorA=pointInSpace, vectorB=lineStartPoint)  # Find vector from point in space to the start of the line
    dot = vecDot(vectorA=ac, vectorB=ba) # get the dotProduct between ac and ba
    percent = dot / l2 # Find petcentage from start to end point
   
    # if percent value is less than 0.0 or greater than 1.0, then the point in space outside of the line segment - exclude them
    if ignoreNoProjections == True:
        if percent < 0.0 or percent > 1.0:
            return [0.0, 0.0, 0.0] # Return a zero vector
   
    point = vecAdd(vectorA=lineStartPoint, vectorB=vecMultScalar(scalar=percent, vector=ac)) # Now we can find the closest point
    return point

Or use a nearestPointOnCurve node and when done - delete it.

Cheers

Sasha

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[s...@weacceptyou.com]

thanks Sasha, very interesting will try this out thanks,

Sam