workplane.py

#!/usr/bin/env python
#
# Copyright 2020 Doug Blanding (dblanding@gmail.com)
#
# This file is part of cadViewer.
# The latest  version of this file can be found at:
# //https://github.com/dblanding/cadviewer
#
# cadViewer is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# cadViewer is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# if not, write to the Free Software Foundation, Inc.
# 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#

import math
from OCC.Core.BRepBuilderAPI import (BRepBuilderAPI_MakeEdge,
                                     BRepBuilderAPI_MakeFace,
                                     BRepBuilderAPI_MakeWire)
from OCC.Core.BRepGProp import brepgprop_SurfaceProperties
from OCC.Core.GC import GC_MakeArcOfCircle, GC_MakeSegment
from OCC.Core.Geom2d import Geom2d_Circle, Geom2d_Line
from OCC.Core.Geom2dAPI import Geom2dAPI_InterCurveCurve
from OCC.Core.Geom import Geom_Circle, Geom_Plane, Geom_Line
from OCC.Core.gp import (gp_Ax2, gp_Ax3, gp_Dir, gp_Dir2d, gp_Lin2d, gp_Pnt,
                         gp_Pnt2d, gp_Ax2d, gp_Circ2d, gp_Pln, gp_Trsf, gp_Vec)
from OCC.Core.GProp import GProp_GProps
from OCCUtils.Construct import face_normal
from OCC.Core.TopTools import TopTools_ListOfShape

INFINITY = 1e+10  # mm (on the order of Earth's diameter)

#===========================================================================
#
# Math & geometry 2D utility functions
#
#===========================================================================

def intersection(cline1, cline2):
    """Return intersection (x,y) of 2 clines expressed as (a,b,c) coeff."""
    a, b, c = cline1
    d, e, f = cline2
    i = b*f - c*e
    j = c*d - a*f
    k = a*e - b*d
    if k:
        return (i/k, j/k)
    return None

def cnvrt_2pts_to_coef(pt1, pt2):
    """Return (a,b,c) coefficients of cline defined by 2 (x,y) pts."""
    x1, y1 = pt1
    x2, y2 = pt2
    a = y2 - y1
    b = x1 - x2
    c = x2*y1-x1*y2
    return (a, b, c)

def proj_pt_on_line(cline, pt):
    """Return point which is the projection of pt on cline."""
    a, b, c = cline
    x, y = pt
    denom = a**2 + b**2
    if not denom:
        return pt
    xp = (b**2*x - a*b*y -a*c)/denom
    yp = (a**2*y - a*b*x -b*c)/denom
    return (xp, yp)

def pnt_in_box_p(pnt, box):
    '''Point in box predicate: Return True if pnt is in box.'''
    x, y = pnt
    x1, y1, x2, y2 = box
    if x1 < x < x2 and y1 < y < y2:
        return True

def midpoint(p1, p2, f=.5):
    """Return point part way (f=.5 by def) between points p1 and p2."""
    return (((p2[0]-p1[0])*f)+p1[0], ((p2[1]-p1[1])*f)+p1[1])

def p2p_dist(p1, p2):
    """Return the distance between two points"""
    x, y = p1
    u, v = p2
    return math.sqrt((x-u)**2 + (y-v)**2)

def p2p_angle(p0, p1):
    """Return angle (degrees) from p0 to p1."""
    return math.atan2(p1[1]-p0[1], p1[0]-p0[0])*180/math.pi

def add_pt(p0, p1):
    return (p0[0]+p1[0], p0[1]+p1[1])

def sub_pt(p0, p1):
    return (p0[0]-p1[0], p0[1]-p1[1])

def seg_circ_inters(x1, y1, x2, y2, xc, yc, r):
    '''Return list of intersection pts of line defined by pts x1,y1 and x2,y2
    and circle (cntr xc,yc and radius r).
    Uses algorithm from Paul Bourke's web page.'''
    intpnts = []
    num = (xc - x1)*(x2 - x1) + (yc - y1)*(y2 - y1)
    denom = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1)
    if denom == 0:
        return
    u = num / denom
    xp = x1 + u*(x2-x1)
    yp = y1 + u*(y2-y1)

    a = (x2 - x1)**2 + (y2 - y1)**2
    b = 2*((x2-x1)*(x1-xc) + (y2-y1)*(y1-yc))
    c = xc**2+yc**2+x1**2+y1**2-2*(xc*x1+yc*y1)-r**2
    q = b**2 - 4*a*c
    if q == 0:
        intpnts.append((xp, yp))
    elif q:
        u1 = (-b+math.sqrt(abs(q)))/(2*a)
        u2 = (-b-math.sqrt(abs(q)))/(2*a)
        intpnts.append(((x1 + u1*(x2-x1)), (y1 + u1*(y2-y1))))
        intpnts.append(((x1 + u2*(x2-x1)), (y1 + u2*(y2-y1))))
    return intpnts

def line_circ_inters(line, circle):
    '''Return list of intersection pts of line and circle.

    line defined by coeffs a, b, c, circle (cntr xc,yc and radius r)
    Doesn't work right. It comes up with some extra points.'''
    a, b, c = line
    (xc, yc), r = circle
    # first find pt on line closest to circle center
    p0 = proj_pt_on_line(line, (xc, yc))
    # define corners of box (4r x 4r) centered on p0
    x0, y0 = p0
    xb1 = x0 - 2*r
    yb1 = y0 - 2*r
    xb2 = x0 + 2*r
    yb2 = y0 + 2*r
    box = (xb1, yb1, xb2, yb2)
    # define line segment to be intersection points of line with box
    p1, p2 = cline_box_intrsctn(line, box)
    x1, y1 = p1
    x2, y2 = p2
    # find intersection points of segment and circle
    return seg_circ_inters(x1, y1, x2, y2, xc, yc, r)

def circ_circ_inters(circ1, circ2):
    '''Return list of intersection pts of 2 circles.
    Uses algorithm from Robert S. Wilson's web page.'''
    (x1, y1), r1 = circ1
    (x2, y2), r2 = circ2
    pts = []
    D = (x2-x1)**2 + (y2-y1)**2
    if not D:
        return pts  # circles have same cntr; no intersection
    try:
        q = math.sqrt(abs(((r1+r2)**2-D)*(D-(r2-r1)**2)))
    except:
        return pts  # circles don't interect
    pts = [((x2+x1)/2+(x2-x1)*(r1**2-r2**2)/(2*D)+(y2-y1)*q/(2*D),
            (y2+y1)/2+(y2-y1)*(r1**2-r2**2)/(2*D)-(x2-x1)*q/(2*D)),
           ((x2+x1)/2+(x2-x1)*(r1**2-r2**2)/(2*D)-(y2-y1)*q/(2*D),
            (y2+y1)/2+(y2-y1)*(r1**2-r2**2)/(2*D)+(x2-x1)*q/(2*D))]
    if same_pt_p(pts[0], pts[1]):
        pts.pop()   # circles are tangent
    return pts

def same_pt_p(p1, p2):
    '''Return True if p1 and p2 are within 1e-10 of each other.'''
    if p2p_dist(p1, p2) < 1e-6:
        return True

def cline_box_intrsctn(cline, box):
    """Return tuple of pts where line intersects edges of box."""
    x0, y0, x1, y1 = box
    pts = []
    segments = [((x0, y0), (x1, y0)),
                ((x1, y0), (x1, y1)),
                ((x1, y1), (x0, y1)),
                ((x0, y1), (x0, y0))]
    for seg in segments:
        pt = intersection(cline, cnvrt_2pts_to_coef(seg[0], seg[1]))
        if pt:
            if p2p_dist(pt, seg[0]) <= p2p_dist(seg[0], seg[1]) and \
               p2p_dist(pt, seg[1]) <= p2p_dist(seg[0], seg[1]):
                if pt not in pts:
                    pts.append(pt)
    return tuple(pts)

def para_line(cline, pt):
    """Return coeff of newline thru pt and parallel to cline."""
    a, b, c = cline
    x, y = pt
    cnew = -(a*x + b*y)
    return (a, b, cnew)

def para_lines(cline, d):
    """Return 2 parallel lines straddling line, offset d."""
    a, b, c = cline
    c1 = math.sqrt(a**2 + b**2)*d
    cline1 = (a, b, c + c1)
    cline2 = (a, b, c - c1)
    return (cline1, cline2)

def perp_line(cline, pt):
    """Return coeff of newline thru pt and perpend to cline."""
    a, b, c = cline
    x, y = pt
    cnew = a*y - b*x
    return (b, -a, cnew)

def closer(p0, p1, p2):
    """Return closer of p1 or p2 to point p0."""
    d1 = (p1[0] - p0[0])**2 + (p1[1] - p0[1])**2
    d2 = (p2[0] - p0[0])**2 + (p2[1] - p0[1])**2
    if d1 < d2:
        return p1
    return p2

def farther(p0, p1, p2):
    """Return farther of p1 or p2 from point p0."""
    d1 = (p1[0] - p0[0])**2 + (p1[1] - p0[1])**2
    d2 = (p2[0] - p0[0])**2 + (p2[1] - p0[1])**2
    if d1 > d2:
        return p1
    return p2

def find_fillet_pts(r, commonpt, end1, end2):
    """Return ctr of fillet (radius r) and tangent pts for corner
    defined by a common pt, and two adjacent corner pts."""
    line1 = cnvrt_2pts_to_coef(commonpt, end1)
    line2 = cnvrt_2pts_to_coef(commonpt, end2)
    # find 'interior' clines
    cl1a, cl1b = para_lines(line1, r)
    p2a = proj_pt_on_line(cl1a, end2)
    p2b = proj_pt_on_line(cl1b, end2)
    da = p2p_dist(p2a, end2)
    db = p2p_dist(p2b, end2)
    if da <= db: cl1 = cl1a
    else: cl1 = cl1b
    cl2a, cl2b = para_lines(line2, r)
    p1a = proj_pt_on_line(cl2a, end1)
    p1b = proj_pt_on_line(cl2b, end1)
    da = p2p_dist(p1a, end1)
    db = p2p_dist(p1b, end1)
    if da <= db:
        cl2 = cl2a
    else:
        cl2 = cl2b
    pc = intersection(cl1, cl2)
    p1 = proj_pt_on_line(line1, pc)
    p2 = proj_pt_on_line(line2, pc)
    return (pc, p1, p2)

def find_common_pt(apair, bpair):
    """Return (common pt, other pt from a, other pt from b), where a and b
    are coordinate pt pairs in (p1, p2) format."""
    p0, p1 = apair
    p2, p3 = bpair
    if same_pt_p(p0, p2):
        cp = p0     # common pt
        opa = p1    # other pt a
        opb = p3    # other pt b
    elif same_pt_p(p0, p3):
        cp = p0
        opa = p1
        opb = p2
    elif same_pt_p(p1, p2):
        cp = p1
        opa = p0
        opb = p3
    elif same_pt_p(p1, p3):
        cp = p1
        opa = p0
        opb = p2
    else:
        return
    return (cp, opa, opb)

def cr_from_3p(p1, p2, p3):
    """Return ctr pt and radius of circle on which 3 pts reside.
    From Paul Bourke's web page."""
    chord1 = cnvrt_2pts_to_coef(p1, p2)
    chord2 = cnvrt_2pts_to_coef(p2, p3)
    radial_line1 = perp_line(chord1, midpoint(p1, p2))
    radial_line2 = perp_line(chord2, midpoint(p2, p3))
    ctr = intersection(radial_line1, radial_line2)
    if ctr:
        radius = p2p_dist(p1, ctr)
        return (ctr, radius)

def extendline(p0, p1, d):
    """Return point which lies on extension of line segment p0-p1,
    beyond p1 by distance d."""
    pts = seg_circ_inters(p0[0], p0[1], p1[0], p1[1], p1[0], p1[1], d)
    if pts:
        return farther(p0, pts[0], pts[1])

def shortenline(p0, p1, d):
    """Return point which lies on line segment p0-p1,
    short of p1 by distance d."""
    pts = seg_circ_inters(p0[0], p0[1], p1[0], p1[1], p1[0], p1[1], d)
    if pts:
        return closer(p0, pts[0], pts[1])

def line_tan_to_circ(circ, p):
    """Return tan pts on circ of line through p."""
    c, r = circ
    d = p2p_dist(c, p)
    ang0 = p2p_angle(c, p)*math.pi/180
    theta = math.asin(r/d)
    ang1 = ang0+math.pi/2-theta
    ang2 = ang0-math.pi/2+theta
    p1 = (c[0]+(r*math.cos(ang1)), c[1]+(r*math.sin(ang1)))
    p2 = (c[0]+(r*math.cos(ang2)), c[1]+(r*math.sin(ang2)))
    return (p1, p2)

def line_tan_to_2circs(circ1, circ2):
    """Return tangent pts on line tangent to 2 circles.
    Order of circle picks determines which tangent line."""
    c1, r1 = circ1
    c2, r2 = circ2
    d = p2p_dist(c1, c2)    # distance between centers
    ang_loc = p2p_angle(c2, c1)*math.pi/180  # angle of line of centers
    f = (r2/r1-1)/d # reciprocal dist from c1 to intersection of loc & tan line
    theta = math.asin(r1*f)    # angle between loc and tangent line
    ang1 = (ang_loc + math.pi/2 - theta)
    ang2 = (ang_loc - math.pi/2 + theta)
    p1 = (c1[0]+(r1*math.cos(ang1)), c1[1]+(r1*math.sin(ang1)))
    p2 = (c2[0]+(r2*math.cos(ang1)), c2[1]+(r2*math.sin(ang1)))
    return (p1, p2)

def angled_cline(pt, angle):
    """Return cline through pt at angle (degrees)"""
    ang = angle * math.pi / 180
    dx = math.cos(ang)
    dy = math.sin(ang)
    p2 = (pt[0]+dx, pt[1]+dy)
    cline = cnvrt_2pts_to_coef(pt, p2)
    return cline

def ang_bisector(p0, p1, p2, f=0.5):
    """Return cline coefficients of line through vertex p0, factor=f
    between p1 and p2."""
    ang1 = math.atan2(p1[1]-p0[1], p1[0]-p0[0])
    ang2 = math.atan2(p2[1]-p0[1], p2[0]-p0[0])
    deltang = ang2 - ang1
    ang3 = (f * deltang + ang1)*180/math.pi
    return angled_cline(p0, ang3)


def pt_on_RHS_p(pt, p0, p1):
    """Return True if pt is on right hand side going from p0 to p1."""
    angline = p2p_angle(p0, p1)
    angpt = p2p_angle(p0, pt)
    if angline >= 0:
        if angline > angpt > angline-180:
            return True
    else:
        angline += 360
        if angpt < 0:
            angpt += 360
        if angline > angpt > angline-180:
            return True

def rotate_pt(pt, ang, ctr):
    """Return coordinates of pt rotated ang (deg) CCW about ctr.
    This is a 3-step process:
    1. translate to place ctr at origin.
    2. rotate about origin (CCW version of Paul Bourke's algorithm.
    3. apply inverse translation. """
    x, y = sub_pt(pt, ctr)
    A = ang * math.pi / 180
    u = x * math.cos(A) - y * math.sin(A)
    v = y * math.cos(A) + x * math.sin(A)
    return add_pt((u, v), ctr)

#===========================================================================

class WorkPlane():
    """A 2D plane for creating 2D 'Profiles' for building or modifying 3D geometry.

    In addition to profile geometry, the workplane also contains 'construction'
    geometry, useful in making an accurate layout.

    There are three typical ways for creating a new workplane:
    1- Lying on an existing face, with U-dir specified by normal dir of another face
    2- By specification of a gp_Ax3 axis
    3- Default (located with U,V,W aligned with X,Y,Z)
    """
    def __init__(self, size, face=None, faceU=None, ax3=None):
        # gp_Ax3 of XYZ coord system
        origin = gp_Pnt(0, 0, 0)
        wDir = gp_Dir(0, 0, 1)
        uDir = gp_Dir(1, 0, 0)
        vDir = gp_Dir(0, 1, 0)
        xyzAx3 = gp_Ax3(origin, wDir, uDir)
        if (not face and not ax3):  # create default wp (in XY plane at 0,0,0)
            axis3 = xyzAx3
            gpPlane = gp_Pln(xyzAx3)
            self.gpPlane = gpPlane              # type: gp_Pln
            self.plane = Geom_Plane(gpPlane)    # type: Geom_Plane
        elif face:  # create workplane on face, uDir defined by faceU
            wDir = face_normal(face)  # from OCCUtils.Construct module
            props = GProp_GProps()
            brepgprop_SurfaceProperties(face, props)
            origin = props.CentreOfMass()
            uDir = face_normal(faceU)  # from OCCUtils.Construct module
            axis3 = gp_Ax3(origin, wDir, uDir)
            vDir = axis3.YDirection()
            self.gpPlane = gp_Pln(axis3)
            self.plane = Geom_Plane(self.gpPlane)    # type: Geom_Plane
        elif ax3:
            axis3 = ax3
            uDir = axis3.XDirection()
            vDir = axis3.YDirection()
            wDir = axis3.Axis().Direction()
            origin = axis3.Location()
            self.gpPlane = gp_Pln(axis3)
            self.plane = Geom_Plane(self.gpPlane)    # type: Geom_Plane

        self.Trsf = gp_Trsf()
        self.Trsf.SetTransformation(axis3)
        self.Trsf.Invert()
        self.origin = origin
        self.uDir = uDir
        self.vDir = vDir
        self.wDir = wDir
        self.wVec = gp_Vec(wDir)
        self.face = face
        self.size = size
        self.border = self.makeWpBorder(self.size)
        self.clines = set() # set of c-lines with (a, b, c) coefficients
        self.ccircs = set() # set of c-circs with (pc, r) coefficients
        self.edgeList = [] # List of profile lines type: <TopoDS_Edge>
        self.wire = None
        self.accuracy = 1e-6   # min distance between two points
        self.hvcl((0, 0))    # Make H-V clines through origin

    def makeSqProfile(self, size):
        # points and segments need to be in CW sequence to get W pointing along Z
        p1 = gp_Pnt(-size, size, 0).Transformed(self.Trsf)
        p2 = gp_Pnt(size, size, 0).Transformed(self.Trsf)
        p3 = gp_Pnt(size, -size, 0).Transformed(self.Trsf)
        p4 = gp_Pnt(-size, -size, 0).Transformed(self.Trsf)
        seg1 = GC_MakeSegment(p1, p2).Value()
        seg2 = GC_MakeSegment(p2, p3).Value()
        seg3 = GC_MakeSegment(p3, p4).Value()
        seg4 = GC_MakeSegment(p4, p1).Value()
        e1 = BRepBuilderAPI_MakeEdge(seg1).Edge()
        e2 = BRepBuilderAPI_MakeEdge(seg2).Edge()
        e3 = BRepBuilderAPI_MakeEdge(seg3).Edge()
        e4 = BRepBuilderAPI_MakeEdge(seg4).Edge()
        aWire_mkr = BRepBuilderAPI_MakeWire(e1, e2, e3, e4)
        myWireProfile = aWire_mkr.Wire()
        return myWireProfile  # TopoDS_Wire

    def makeWpBorder(self, size):
        wireProfile = self.makeSqProfile(size)
        myFaceProfile = BRepBuilderAPI_MakeFace(wireProfile)
        if myFaceProfile.IsDone():
            border = myFaceProfile.Face()
        return border  # TopoDS_Face

    #=======================================================================
    # Utility functions (Relayed)
    #=======================================================================

    def p2p_dist(self, p1, p2):
        return p2p_dist(p1, p2)

    #=======================================================================
    # Construction Geometry
    # construction lines (clines) are "infinite" length lines
    # described by the equation:        ax + by + c = 0
    # defined by coefficients:          (a, b, c)
    # In order to have a nice display of a cline, an 'AIS_Line' is used.
    # To create an 'AIS_Line', type 'Geom_Line' is needed.
    #
    # circles are defined by coordinates:   (pc, r)
    # In order to have a nice display of a ccirc, an 'AIS_Circle' is used.
    # To create an 'AIS_Circle', type 'Geom_Circle' is needed.
    # In order to find intersection points (x, y), 'Geom2d_Circle' is needed.
    # Methods are provided to generate all the various types needed.
    #=======================================================================

    def cline_gen(self, cline):
        a, b, c = cline
        unique = True
        for d, e, f in self.clines:
            if (abs(a-d) < self.accuracy and\
                abs(b-e) < self.accuracy and\
                abs(c-f) < self.accuracy):
                unique = False
                break
        if unique:
            self.clines.add(cline)

    def geom2dLines(self):
        """Return self.clines as list of type: <Geom2d_Line>."""
        return [Geom2d_Line(gp_Lin2d(*cline)) for cline in self.clines]

    def geomLineBldr(self, cline):
        """Convert native cline to type: <Geom_Line>."""
        a, b, c = cline
        gpLin2d = gp_Lin2d(a, b, c)
        gpDir2d = gpLin2d.Direction()
        gpPnt2d = gpLin2d.Location()
        gpPnt = gp_Pnt(gpPnt2d.X(), gpPnt2d.Y(), 0).Transformed(self.Trsf)
        gpDir = gp_Dir(gpDir2d.X(), gpDir2d.Y(), 0).Transformed(self.Trsf)
        return Geom_Line(gpPnt, gpDir)

    def geomLines(self):
        """Return self.clines as list of type: <Geom_Line>."""
        return [self.geomLineBldr(cline) for cline in self.clines]

    def hcl(self, pnt=None):
        """Create horizontal construction line from a point (x,y)."""
        if pnt:
            cline = angled_cline(pnt, 0)
            self.cline_gen(cline)

    def vcl(self, pnt=None):
        """Create vertical construction line from a point (x,y)."""
        if pnt:
            cline = angled_cline(pnt, 90)
            self.cline_gen(cline)

    def hvcl(self, pnt=None):
        """Create a horiz & vert construction line pair at a point."""
        if pnt:
            self.cline_gen(angled_cline(pnt, 0))
            self.cline_gen(angled_cline(pnt, 90))

    def acl(self, pnt1, pnt2=None, ang=None):
        """Create a construction line thru a first point, then through
        a second specified point or at a specified angle."""
        if pnt1 and pnt2:
            cline = cnvrt_2pts_to_coef(pnt1, pnt2)
            self.cline_gen(cline)
        elif pnt1 and ang:
            cline = angled_cline(pnt1, ang)
            self.cline_gen(cline)

    def lbcl(self, p1, p2, f=.5):
        """Create a linear bisector construction line."""
        p0 = midpoint(p1, p2, f)
        baseline = cnvrt_2pts_to_coef(p1, p2)
        newline = perp_line(baseline, p0)
        self.cline_gen(newline)

    def unique(self, point, points):
        """boolean test for uniqueness within collection."""
        x0, y0 = point
        unique = True
        for x, y in points:
            if (abs(x - x0) < self.accuracy and abs(y - y0) < self.accuracy):
                unique = False
                break
        return unique

    def intersectPts(self):
        """List of intersection points among c-lines & c-circs"""

        points = set()  # set of intersections as (x, y) 2d points

        # find intersection points of clines with ccircs
        for ccirc in self.geom2dCircs():  # type Geom2d_Circle
            for cline in self.geom2dLines():  # type Geom2d_Line
                inters = Geom2dAPI_InterCurveCurve(ccirc, cline)
                if inters.NbPoints():
                    candidates = []
                    for i in range(inters.NbPoints()):
                        pnt2d = inters.Point(i+1)  # OCC type 2d point
                        point = (pnt2d.X(), pnt2d.Y())  # simple (x, y) point
                        candidates.append(point)
                    for pnt in candidates:
                        if self.unique(pnt, points):
                            points.add(pnt)

        # find intersection points among ccircs
        ccirc2dList = list(self.ccircs)  # copy list
        for i in range(len(self.ccircs)):
            circ0 = ccirc2dList.pop()
            for circ in ccirc2dList:
                inters = circ_circ_inters(circ0, circ)
                for pnt in inters:
                    if self.unique(pnt, points):
                        points.add(pnt)

        # find intersection points among clines
        clList = list(self.clines) # list of (a, b, c) 2d lines
        newpoints = []  # new finite points
        for i in range(len(clList)):
            line0 = clList.pop()
            for line in clList:
                P = intersection(line0, line)
                if P:  # P is not None
                    if (not points and abs(P[0]) < INFINITY and\
                        abs(P[1]) < INFINITY):
                        points.add(P) # first point, (not at inf.)
                    else:
                        if abs(P[0]) < INFINITY and abs(P[1]) < INFINITY:
                            newpoints.append(P)
        for pnt in newpoints:
            if self.unique(pnt, points):
                points.add(pnt)

        # convert 2d points to 3d
        pntList = []
        for point in points:
            if point:  # exclude 'None' types
                x, y = point
                pnt = gp_Pnt(x, y, 0)
                pnt.Transform(self.Trsf)
                pntList.append(pnt)
        return pntList

    #=======================================================================
    # Profile Geometry
    # Profile lines are type 'TopoDS_Edge' lines, circles and arcs.
    # They will eventually get 'collected' into a closed loop and then used
    # to build a wire (type 'TopoDS_Wire'), which can then be used as a tool
    # to extrude or cut a solid body.
    #=======================================================================

    def line(self, pnt1, pnt2):
        """Create a line between two end points."""
        # Two 2d end points
        x1, y1 = pnt1
        x2, y2 = pnt2
        p1 = gp_Pnt(x1, y1, 0).Transformed(self.Trsf)
        p2 = gp_Pnt(x2, y2, 0).Transformed(self.Trsf)
        seg = GC_MakeSegment(p1, p2).Value()  # Geom_TrimmedCurve
        # Build the edge
        edge = BRepBuilderAPI_MakeEdge(seg).Edge()  # TopoDS_Edge
        self.edgeList.append(edge)


    def rect(self, pnt1, pnt2):
        """Create a rectangle from two diagonally opposite corners."""
        # 2 diagonally opposite corners
        x1, y1 = pnt1
        x2, y2 = pnt2
        # 4 corners of rectangle
        p1 = gp_Pnt(x1, y1, 0).Transformed(self.Trsf)
        p2 = gp_Pnt(x2, y1, 0).Transformed(self.Trsf)
        p3 = gp_Pnt(x2, y2, 0).Transformed(self.Trsf)
        p4 = gp_Pnt(x1, y2, 0).Transformed(self.Trsf)
        # 4 sides (segments) of rectangle
        seg1 = GC_MakeSegment(p1, p2).Value()  # Geom_TrimmedCurve
        seg2 = GC_MakeSegment(p2, p3).Value()
        seg3 = GC_MakeSegment(p3, p4).Value()
        seg4 = GC_MakeSegment(p4, p1).Value()
        # Build the edges
        e1 = BRepBuilderAPI_MakeEdge(seg1).Edge()  # TopoDS_Edge
        e2 = BRepBuilderAPI_MakeEdge(seg2).Edge()
        e3 = BRepBuilderAPI_MakeEdge(seg3).Edge()
        e4 = BRepBuilderAPI_MakeEdge(seg4).Edge()
        edges = (e1, e2, e3, e4)
        for edge in edges:
            self.edgeList.append(edge)

    def circle(self, cntr, rad, constr=False):
        """Create a circle (constr or profile)"""
        circ = (cntr, rad)
        if constr:
            self.ccircs.add(circ)
            self.hvcl(cntr)
        else:
            edge = BRepBuilderAPI_MakeEdge(self.convert_circ_to_geomCirc(circ)).Edge()
            self.edgeList.append(edge)

    def convert_circ_to_geomCirc(self, circ):
        """Convert 2d circle ((cx, cy), r) to type <Geom_Circle>"""
        (cx, cy), rad = circ
        cntrPt = gp_Pnt(cx, cy, 0)
        ax2 = gp_Ax2(cntrPt, gp_Dir(0, 0, 1))
        geomCirc = Geom_Circle(ax2, rad)
        geomCirc.Transform(self.Trsf)
        return geomCirc

    def convert_circ_to_geom2dCirc(self, circ):
        (cx, cy), r = circ
        return Geom2d_Circle(gp_Circ2d(gp_Ax2d(gp_Pnt2d(cx, cy),
                                               gp_Dir2d(1, 0)), r))

    def geom2dCircs(self):
        """Return self.ccircs as type Geom2d_Circles."""
        return [self.convert_circ_to_geom2dCirc(circ)
                for circ in self.ccircs]

    def arcc2p(self, pc, ps, pe):
        """Create an arc from center pt, start pt and end pt."""
        rad = p2p_dist(pc, ps)
        circ2d = (pc, rad)
        geom_circ = self.convert_circ_to_geomCirc(circ2d)
        gp_circ = geom_circ.Circ()
        gp_ps = gp_Pnt(ps[0], ps[1], 0).Transformed(self.Trsf)
        gp_pe = gp_Pnt(pe[0], pe[1], 0).Transformed(self.Trsf)
        geom_arc = GC_MakeArcOfCircle(gp_circ, gp_ps, gp_pe, True).Value()
        edge = BRepBuilderAPI_MakeEdge(geom_arc).Edge()
        self.edgeList.append(edge)

    def arc3p(self, ps, pe, p3):
        """Create an arc from start pt, end pt, and 3rd pt on the arc."""
        gp_ps = gp_Pnt(ps[0], ps[1], 0).Transformed(self.Trsf)
        gp_pe = gp_Pnt(pe[0], pe[1], 0).Transformed(self.Trsf)
        gp_p3 = gp_Pnt(p3[0], p3[1], 0).Transformed(self.Trsf)
        geom_arc = GC_MakeArcOfCircle(gp_ps, gp_pe, gp_p3).Value()
        edge = BRepBuilderAPI_MakeEdge(geom_arc).Edge()
        self.edgeList.append(edge)

    #=======================================================================
    # Topo_DS_Wire
    # This is the end result of the workplane: To generate a Topo_DS_Wire
    # Which can be used as a tool to build or modify a face or solid body.
    #=======================================================================

    def makeWire(self):
        """Generate a wire from the edges in self.edgeList."""
        wireBldr = BRepBuilderAPI_MakeWire()
        occ_seq = TopTools_ListOfShape()
        for edge in self.edgeList:
            occ_seq.Append(edge)
        wireBldr.Add(occ_seq)
        if wireBldr.IsDone():
            self.wire = wireBldr.Wire()
            status = True
        else:
            status = False
        return status