meshlabxml/transform.py
def bend(script, radius=1, pitch=0, taper=0, angle=0, straght_start=True,
         straght_end=False, radius_limit=None, outside_limit_end=True):
    """Bends mesh around cylinder of radius radius and axis z to a certain angle

    straight_ends: Only apply twist (pitch) over the area that is bent

    outside_limit_end (bool): should values outside of the bend radius_limit be considered part
        of the end (True) or the start (False)?
    """
    if radius_limit is None:
        radius_limit = 2 * radius
    # TODO: add limit so bend only applies over y<2*radius; add option to set
    # larger limit
    angle = math.radians(angle)
    segment = radius * angle
    """vert_function(s=s, x='if(x<%s and x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(%s/%s)+(x-%s)*cos(%s/%s))'
                        % (segment, segment,  radius, radius,  radius, segment, radius, segment, segment, radius),
                     y='if(x<%s*%s/2 and x>-%s*%s/2, (%s+y)*cos(x/%s), (%s+y)*cos(%s)-(x-%s*%s)*sin(%s))'
                        % (radius, angle, radius, angle, radius, radius, radius, angle/2, radius, angle/2, angle/2),"""
    pitch_func = '-(pitch)*x/(2*pi*(radius))'.replace(
        'pitch', str(pitch)).replace(
            'pi', str(math.pi)).replace(
                'radius', str(radius))
    taper_func = '(taper)*(pitch_func)'.replace(
        'taper', str(taper)).replace(
            'pitch_func', str(pitch_func)).replace(
                'pi', str(math.pi))
    # y<radius_limit

    if outside_limit_end:
        x_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*sin(x/(radius)), x), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle))'
    else:
        x_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*sin(x/(radius)), x), if(y<(radius_limit), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle), x))'

    x_func = x_func.replace(
        # x_func = 'if(x<segment, if(x>0, (y+radius)*sin(x/radius), x),
        # (y+radius)*sin(angle)-segment)'.replace(
        'segment', str(segment)).replace(
            'radius_limit', str(radius_limit)).replace(
                'radius', str(radius)).replace(
                    'taper_func', str(taper_func)).replace(
                        'angle', str(angle))

    if outside_limit_end:
        y_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius))'
    else:
        y_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), if(y<(radius_limit), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius), y))'

    y_func = y_func.replace(
        'segment', str(segment)).replace(
            'radius_limit', str(radius_limit)).replace(
                'radius', str(radius)).replace(
                    'taper_func', str(taper_func)).replace(
                        'angle', str(angle))

    if straght_start:
        start = 'z'
    else:
        start = 'z+(pitch_func)'
    if straght_end:
        end = 'z-(pitch)*(angle)/(2*pi)'
    else:
        end = 'z+(pitch_func)'

    if outside_limit_end:
        z_func = 'if(x<(segment) and y<(radius_limit), if(x>0, z+(pitch_func), (start)), (end))'
    else:
        z_func = 'if(x<(segment), if(x>0 and y<(radius_limit), z+(pitch_func), (start)), if(y<(radius_limit), (end), z))'
    z_func = z_func.replace(
        'start', str(start)).replace(
            'end', str(end)).replace(
                'segment', str(segment)).replace(
                    'radius_limit', str(radius_limit)).replace(
                        'radius', str(radius)).replace(
                            'angle', str(angle)).replace(
                                'pitch_func', str(pitch_func)).replace(
                                    'pitch', str(pitch)).replace(
                                        'pi', str(math.pi))

    """
    if straight_ends:
        z_func = 'if(x<segment, if(x>0, z+(pitch_func), z), z-pitch*angle/(2*pi))'.replace(
            'segment', str(segment)).replace(
            'radius', str(radius)).replace(
            'angle', str(angle)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    else:
        #z_func = 'if(x<segment, z+(pitch_func), z-(taper)*(pitch)*(x)/(2*pi*(radius)))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func))'.replace(
        #bestz_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*(x-segment)/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*x/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+((taper)*pitch*angle/(2*pi)))'.replace(
        z_func = 'z+(pitch_func)'.replace(
            'radius', str(radius)).replace(
            'segment', str(segment)).replace(
            'angle', str(angle)).replace(
            'taper', str(taper)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    """
    """
    x_func = 'if(x<%s, if(x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(-%s)+(x+%s)*cos(-%s)), (%s+y)*sin(%s)+(x-%s)*cos(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    y_func = 'if(x<%s, if(x>-%s, (%s+y)*cos(x/%s), (%s+y)*cos(-%s)-(x+%s)*sin(-%s)), (%s+y)*cos(%s)-(x-%s)*sin(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    if straight_ends:
        z_func = 'if(x<%s, if(x>-%s, z-%s*x/(2*%s*%s), z+%s*%s/(2*%s)), z-%s*%s/(2*%s))' % (
            segment, segment, pitch, math.pi, radius, pitch, angle, math.pi, pitch, angle, math.pi)
    else:
        z_func = 'z-%s*x/(2*%s*%s)' % (pitch, math.pi, radius)
    """
    vert_function(script, x_func=x_func, y_func=y_func, z_func=z_func)
    return None
def bend(script, radius=1, pitch=0, taper=0, angle=0, straght_start=True,
         straght_end=False, radius_limit=None, outside_limit_end=True):
    if radius_limit is None:
        radius_limit = 2 * radius
    # TODO: add limit so bend only applies over y<2*radius; add option to set
    # larger limit
    angle = math.radians(angle)
    segment = radius * angle
    """vert_function(s=s, x='if(x<%s and x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(%s/%s)+(x-%s)*cos(%s/%s))'
                        % (segment, segment,  radius, radius,  radius, segment, radius, segment, segment, radius),
                     y='if(x<%s*%s/2 and x>-%s*%s/2, (%s+y)*cos(x/%s), (%s+y)*cos(%s)-(x-%s*%s)*sin(%s))'
                        % (radius, angle, radius, angle, radius, radius, radius, angle/2, radius, angle/2, angle/2),"""
    pitch_func = '-(pitch)*x/(2*pi*(radius))'.replace(
        'pitch', str(pitch)).replace(
            'pi', str(math.pi)).replace(
                'radius', str(radius))
    taper_func = '(taper)*(pitch_func)'.replace(
        'taper', str(taper)).replace(
            'pitch_func', str(pitch_func)).replace(
                'pi', str(math.pi))
    # y<radius_limit

    if outside_limit_end:
        x_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*sin(x/(radius)), x), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle))'
    else:
        x_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*sin(x/(radius)), x), if(y<(radius_limit), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle), x))'

    x_func = x_func.replace(
        # x_func = 'if(x<segment, if(x>0, (y+radius)*sin(x/radius), x),
        # (y+radius)*sin(angle)-segment)'.replace(
        'segment', str(segment)).replace(
            'radius_limit', str(radius_limit)).replace(
                'radius', str(radius)).replace(
                    'taper_func', str(taper_func)).replace(
                        'angle', str(angle))

    if outside_limit_end:
        y_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius))'
    else:
        y_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), if(y<(radius_limit), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius), y))'

    y_func = y_func.replace(
        'segment', str(segment)).replace(
            'radius_limit', str(radius_limit)).replace(
                'radius', str(radius)).replace(
                    'taper_func', str(taper_func)).replace(
                        'angle', str(angle))

    if straght_start:
        start = 'z'
    else:
        start = 'z+(pitch_func)'
    if straght_end:
        end = 'z-(pitch)*(angle)/(2*pi)'
    else:
        end = 'z+(pitch_func)'

    if outside_limit_end:
        z_func = 'if(x<(segment) and y<(radius_limit), if(x>0, z+(pitch_func), (start)), (end))'
    else:
        z_func = 'if(x<(segment), if(x>0 and y<(radius_limit), z+(pitch_func), (start)), if(y<(radius_limit), (end), z))'
    z_func = z_func.replace(
        'start', str(start)).replace(
            'end', str(end)).replace(
                'segment', str(segment)).replace(
                    'radius_limit', str(radius_limit)).replace(
                        'radius', str(radius)).replace(
                            'angle', str(angle)).replace(
                                'pitch_func', str(pitch_func)).replace(
                                    'pitch', str(pitch)).replace(
                                        'pi', str(math.pi))

    """
    if straight_ends:
        z_func = 'if(x<segment, if(x>0, z+(pitch_func), z), z-pitch*angle/(2*pi))'.replace(
            'segment', str(segment)).replace(
            'radius', str(radius)).replace(
            'angle', str(angle)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    else:
        #z_func = 'if(x<segment, z+(pitch_func), z-(taper)*(pitch)*(x)/(2*pi*(radius)))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func))'.replace(
        #bestz_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*(x-segment)/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*x/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+((taper)*pitch*angle/(2*pi)))'.replace(
        z_func = 'z+(pitch_func)'.replace(
            'radius', str(radius)).replace(
            'segment', str(segment)).replace(
            'angle', str(angle)).replace(
            'taper', str(taper)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    """
    """
    x_func = 'if(x<%s, if(x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(-%s)+(x+%s)*cos(-%s)), (%s+y)*sin(%s)+(x-%s)*cos(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    y_func = 'if(x<%s, if(x>-%s, (%s+y)*cos(x/%s), (%s+y)*cos(-%s)-(x+%s)*sin(-%s)), (%s+y)*cos(%s)-(x-%s)*sin(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    if straight_ends:
        z_func = 'if(x<%s, if(x>-%s, z-%s*x/(2*%s*%s), z+%s*%s/(2*%s)), z-%s*%s/(2*%s))' % (
            segment, segment, pitch, math.pi, radius, pitch, angle, math.pi, pitch, angle, math.pi)
    else:
        z_func = 'z-%s*x/(2*%s*%s)' % (pitch, math.pi, radius)
    """
    vert_function(script, x_func=x_func, y_func=y_func, z_func=z_func)
    return None
def bend ( script , radius = 1 , pitch = 0 , taper = 0 , angle = 0 , straght_start = True , straght_end = False , radius_limit = None , outside_limit_end = True ) : if radius_limit is None : radius_limit = 2 * radius # TODO: add limit so bend only applies over y<2*radius; add option to set # larger limit angle = math . radians ( angle ) segment = radius * angle """vert_function(s=s, x='if(x<%s and x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(%s/%s)+(x-%s)*cos(%s/%s))'
                        % (segment, segment,  radius, radius,  radius, segment, radius, segment, segment, radius),
                     y='if(x<%s*%s/2 and x>-%s*%s/2, (%s+y)*cos(x/%s), (%s+y)*cos(%s)-(x-%s*%s)*sin(%s))'
                        % (radius, angle, radius, angle, radius, radius, radius, angle/2, radius, angle/2, angle/2),""" pitch_func = '-(pitch)*x/(2*pi*(radius))' . replace ( 'pitch' , str ( pitch ) ) . replace ( 'pi' , str ( math . pi ) ) . replace ( 'radius' , str ( radius ) ) taper_func = '(taper)*(pitch_func)' . replace ( 'taper' , str ( taper ) ) . replace ( 'pitch_func' , str ( pitch_func ) ) . replace ( 'pi' , str ( math . pi ) ) # y<radius_limit if outside_limit_end : x_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*sin(x/(radius)), x), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle))' else : x_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*sin(x/(radius)), x), if(y<(radius_limit), (y+(radius)+(taper_func))*sin(angle)+(x-(segment))*cos(angle), x))' x_func = x_func . replace ( # x_func = 'if(x<segment, if(x>0, (y+radius)*sin(x/radius), x), # (y+radius)*sin(angle)-segment)'.replace( 'segment' , str ( segment ) ) . replace ( 'radius_limit' , str ( radius_limit ) ) . replace ( 'radius' , str ( radius ) ) . replace ( 'taper_func' , str ( taper_func ) ) . replace ( 'angle' , str ( angle ) ) if outside_limit_end : y_func = 'if(x<(segment) and y<(radius_limit), if(x>0, (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius))' else : y_func = 'if(x<(segment), if(x>0 and y<(radius_limit), (y+(radius)+(taper_func))*cos(x/(radius))-(radius), y), if(y<(radius_limit), (y+(radius)+(taper_func))*cos(angle)-(x-(segment))*sin(angle)-(radius), y))' y_func = y_func . replace ( 'segment' , str ( segment ) ) . replace ( 'radius_limit' , str ( radius_limit ) ) . replace ( 'radius' , str ( radius ) ) . replace ( 'taper_func' , str ( taper_func ) ) . replace ( 'angle' , str ( angle ) ) if straght_start : start = 'z' else : start = 'z+(pitch_func)' if straght_end : end = 'z-(pitch)*(angle)/(2*pi)' else : end = 'z+(pitch_func)' if outside_limit_end : z_func = 'if(x<(segment) and y<(radius_limit), if(x>0, z+(pitch_func), (start)), (end))' else : z_func = 'if(x<(segment), if(x>0 and y<(radius_limit), z+(pitch_func), (start)), if(y<(radius_limit), (end), z))' z_func = z_func . replace ( 'start' , str ( start ) ) . replace ( 'end' , str ( end ) ) . replace ( 'segment' , str ( segment ) ) . replace ( 'radius_limit' , str ( radius_limit ) ) . replace ( 'radius' , str ( radius ) ) . replace ( 'angle' , str ( angle ) ) . replace ( 'pitch_func' , str ( pitch_func ) ) . replace ( 'pitch' , str ( pitch ) ) . replace ( 'pi' , str ( math . pi ) ) """
    if straight_ends:
        z_func = 'if(x<segment, if(x>0, z+(pitch_func), z), z-pitch*angle/(2*pi))'.replace(
            'segment', str(segment)).replace(
            'radius', str(radius)).replace(
            'angle', str(angle)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    else:
        #z_func = 'if(x<segment, z+(pitch_func), z-(taper)*(pitch)*(x)/(2*pi*(radius)))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func))'.replace(
        #bestz_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*(x-segment)/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+(-(taper)*(pitch)*x/(2*pi*(radius))))'.replace(
        #z_func = 'if(x<segment, z+(pitch_func), z+(pitch_func)+((taper)*pitch*angle/(2*pi)))'.replace(
        z_func = 'z+(pitch_func)'.replace(
            'radius', str(radius)).replace(
            'segment', str(segment)).replace(
            'angle', str(angle)).replace(
            'taper', str(taper)).replace(
            'pitch_func', str(pitch_func)).replace(
            'pitch', str(pitch)).replace(
            'pi', str(math.pi))
    """ """
    x_func = 'if(x<%s, if(x>-%s, (%s+y)*sin(x/%s), (%s+y)*sin(-%s)+(x+%s)*cos(-%s)), (%s+y)*sin(%s)+(x-%s)*cos(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    y_func = 'if(x<%s, if(x>-%s, (%s+y)*cos(x/%s), (%s+y)*cos(-%s)-(x+%s)*sin(-%s)), (%s+y)*cos(%s)-(x-%s)*sin(%s))' % (
        segment, segment, radius, radius, radius, angle, segment, angle, radius, angle, segment, angle)
    if straight_ends:
        z_func = 'if(x<%s, if(x>-%s, z-%s*x/(2*%s*%s), z+%s*%s/(2*%s)), z-%s*%s/(2*%s))' % (
            segment, segment, pitch, math.pi, radius, pitch, angle, math.pi, pitch, angle, math.pi)
    else:
        z_func = 'z-%s*x/(2*%s*%s)' % (pitch, math.pi, radius)
    """ vert_function ( script , x_func = x_func , y_func = y_func , z_func = z_func ) return None
Bends mesh around cylinder of radius radius and axis z to a certain angle

    straight_ends: Only apply twist (pitch) over the area that is bent

    outside_limit_end (bool): should values outside of the bend radius_limit be considered part
        of the end (True) or the start (False)?
Bends mesh around cylinder of radius radius and axis z to a certain angle