Draft: move more functions to draftgeoutils.circles, part 2
This commit is contained in:
vocx-fc
@@ -371,120 +371,13 @@ from draftgeoutils.circles import circlefrom1Line2Points
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from draftgeoutils.circles import circleFrom2LinesRadius
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def circleFrom3LineTangents(edge1, edge2, edge3):
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"""circleFrom3LineTangents(edge,edge,edge)"""
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def rot(ed):
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return Part.LineSegment(v1(ed),v1(ed).add(DraftVecUtils.rotate(vec(ed),math.pi/2))).toShape()
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bis12 = angleBisection(edge1,edge2)
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bis23 = angleBisection(edge2,edge3)
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bis31 = angleBisection(edge3,edge1)
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intersections = []
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int = findIntersection(bis12, bis23, True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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int = findIntersection(bis23, bis31, True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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int = findIntersection(bis31, bis12, True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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int = findIntersection(rot(bis12), rot(bis23), True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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int = findIntersection(rot(bis23), rot(bis31), True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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int = findIntersection(rot(bis31), rot(bis12), True, True)
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if int:
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radius = findDistance(int[0],edge1).Length
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intersections.append(Part.Circle(int[0],NORM,radius))
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circles = []
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for int in intersections:
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exists = False
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for cir in circles:
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if DraftVecUtils.equals(cir.Center, int.Center):
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exists = True
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break
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if not exists:
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circles.append(int)
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if circles:
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return circles
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else:
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return None
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def circleFromPointLineRadius(point, edge, radius):
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"""circleFromPointLineRadius (point, edge, radius)"""
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dist = findDistance(point, edge, False)
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center1 = None
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center2 = None
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if dist.Length == 0:
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segment = vec(edge)
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perpVec = DraftVecUtils.crossproduct(segment); perpVec.normalize()
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normPoint_c1 = Vector(perpVec).multiply(radius)
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normPoint_c2 = Vector(perpVec).multiply(-radius)
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center1 = point.add(normPoint_c1)
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center2 = point.add(normPoint_c2)
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elif dist.Length > 2 * radius:
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return None
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elif dist.Length == 2 * radius:
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normPoint = point.add(findDistance(point, edge, False))
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dummy = (normPoint.sub(point)).multiply(0.5)
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cen = point.add(dummy)
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circ = Part.Circle(cen, NORM, radius)
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if circ:
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return [circ]
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else:
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return None
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else:
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normPoint = point.add(findDistance(point, edge, False))
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normDist = DraftVecUtils.dist(normPoint, point)
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dist = math.sqrt(radius**2 - (radius - normDist)**2)
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centerNormVec = DraftVecUtils.scaleTo(point.sub(normPoint), radius)
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edgeDir = edge.Vertexes[0].Point.sub(normPoint); edgeDir.normalize()
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center1 = centerNormVec.add(normPoint.add(Vector(edgeDir).multiply(dist)))
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center2 = centerNormVec.add(normPoint.add(Vector(edgeDir).multiply(-dist)))
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circles = []
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if center1:
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circ = Part.Circle(center1, NORM, radius)
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if circ:
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circles.append(circ)
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if center2:
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circ = Part.Circle(center2, NORM, radius)
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if circ:
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circles.append(circ)
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if len(circles):
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return circles
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else:
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return None
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from draftgeoutils.circles import circleFrom3LineTangents
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def circleFrom2PointsRadius(p1, p2, radius):
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"""circleFrom2PointsRadiust(Vector, Vector, radius)"""
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if DraftVecUtils.equals(p1, p2): return None
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from draftgeoutils.circles import circleFromPointLineRadius
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p1_p2 = Part.LineSegment(p1, p2).toShape()
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dist_p1p2 = DraftVecUtils.dist(p1, p1)
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mid = findMidpoint(p1_p2)
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if dist_p1p2 == 2*radius:
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circle = Part.Circle(mid, NORM, radius)
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if circle: return [circle]
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else: return None
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dir = vec(p1_p2); dir.normalize()
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perpDir = dir.cross(Vector(0,0,1)); perpDir.normalize()
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dist = math.sqrt(radius**2 - (dist_p1p2 / 2.0)**2)
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cen1 = Vector.add(mid, Vector(perpDir).multiply(dist))
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cen2 = Vector.add(mid, Vector(perpDir).multiply(-dist))
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circles = []
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if cen1: circles.append(Part.Circle(cen1, NORM, radius))
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if cen2: circles.append(Part.Circle(cen2, NORM, radius))
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if circles: return circles
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else: return None
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from draftgeoutils.circles import circleFrom2PointsRadius
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from draftgeoutils.arcs import arcFrom2Pts
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@@ -661,130 +554,13 @@ from draftgeoutils.linear_algebra import linearFromPoints
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from draftgeoutils.linear_algebra import determinant
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def findHomotheticCenterOfCircles(circle1, circle2):
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"""Calculate the homothetic center(s) of two circles.
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http://en.wikipedia.org/wiki/Homothetic_center
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http://mathworld.wolfram.com/HomotheticCenter.html
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"""
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if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle"):
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if DraftVecUtils.equals(circle1.Curve.Center, circle2.Curve.Center):
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return None
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cen1_cen2 = Part.LineSegment(circle1.Curve.Center, circle2.Curve.Center).toShape()
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cenDir = vec(cen1_cen2); cenDir.normalize()
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# Get the perpedicular vector.
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perpCenDir = cenDir.cross(Vector(0,0,1)); perpCenDir.normalize()
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# Get point on first circle
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p1 = Vector.add(circle1.Curve.Center, Vector(perpCenDir).multiply(circle1.Curve.Radius))
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centers = []
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# Calculate inner homothetic center
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# Get point on second circle
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p2_inner = Vector.add(circle1.Curve.Center, Vector(perpCenDir).multiply(-circle1.Curve.Radius))
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hCenterInner = DraftVecUtils.intersect(circle1.Curve.Center, circle2.Curve.Center, p1, p2_inner, True, True)
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if hCenterInner:
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centers.append(hCenterInner)
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# Calculate outer homothetic center (only exists of the circles have different radii)
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if circle1.Curve.Radius != circle2.Curve.Radius:
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# Get point on second circle
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p2_outer = Vector.add(circle1.Curve.Center, Vector(perpCenDir).multiply(circle1.Curve.Radius))
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hCenterOuter = DraftVecUtils.intersect(circle1.Curve.Center, circle2.Curve.Center, p1, p2_outer, True, True)
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if hCenterOuter:
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centers.append(hCenterOuter)
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if len(centers):
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return centers
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else:
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return None
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else:
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FreeCAD.Console.PrintMessage("debug: findHomotheticCenterOfCirclescleFrom3tan bad parameters!\n")
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return None
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from draftgeoutils.circles import findHomotheticCenterOfCircles
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def findRadicalAxis(circle1, circle2):
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"""Calculate the radical axis of two circles.
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On the radical axis (also called power line) of two circles any
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tangents drawn from a point on the axis to both circles have the same length.
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http://en.wikipedia.org/wiki/Radical_axis
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http://mathworld.wolfram.com/RadicalLine.html
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@sa findRadicalCenter
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"""
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if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle"):
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if DraftVecUtils.equals(circle1.Curve.Center, circle2.Curve.Center):
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return None
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r1 = circle1.Curve.Radius
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r2 = circle1.Curve.Radius
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cen1 = circle1.Curve.Center
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# dist .. the distance from cen1 to cen2.
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dist = DraftVecUtils.dist(cen1, circle2.Curve.Center)
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cenDir = cen1.sub(circle2.Curve.Center); cenDir.normalize()
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# Get the perpedicular vector.
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perpCenDir = cenDir.cross(Vector(0,0,1)); perpCenDir.normalize()
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# J ... The radical center.
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# K ... The point where the cadical axis crosses the line of cen1->cen2.
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# k1 ... Distance from cen1 to K.
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# k2 ... Distance from cen2 to K.
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# dist = k1 + k2
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k1 = (dist + (r1^2 - r2^2) / dist) / 2.0
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#k2 = dist - k1
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K = Vector.add(cen1, cenDir.multiply(k1))
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# K_ .. A point somewhere between K and J (actually with a distance of 1 unit from K).
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K_ = Vector,add(K, perpCenDir)
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radicalAxis = Part.LineSegment(K, Vector.add(origin, dir))
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if radicalAxis:
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return radicalAxis
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else:
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return None
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else:
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FreeCAD.Console.PrintMessage("debug: findRadicalAxis bad parameters!\n")
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return None
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from draftgeoutils.circles import findRadicalAxis
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def findRadicalCenter(circle1, circle2, circle3):
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"""
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findRadicalCenter(circle1, circle2, circle3):
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Calculates the radical center (also called the power center) of three circles.
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It is the intersection point of the three radical axes of the pairs of circles.
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http://en.wikipedia.org/wiki/Power_center_(geometry)
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http://mathworld.wolfram.com/RadicalCenter.html
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@sa findRadicalAxis
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"""
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if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle"):
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radicalAxis12 = findRadicalAxis(circle1, circle2)
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radicalAxis23 = findRadicalAxis(circle1, circle2)
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if not radicalAxis12 or not radicalAxis23:
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# No radical center could be calculated.
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return None
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int = findIntersection(radicalAxis12, radicalAxis23, True, True)
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if int:
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return int
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else:
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# No radical center could be calculated.
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return None
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else:
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FreeCAD.Console.PrintMessage("debug: findRadicalCenter bad parameters!\n")
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return None
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from draftgeoutils.circles import findRadicalCenter
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def pointInversion(circle, point):
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@@ -32,8 +32,8 @@ import lazy_loader.lazy_loader as lz
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import FreeCAD as App
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import DraftVecUtils
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from draftgeoutils.general import geomType, edg, vec, NORM
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from draftgeoutils.geometry import mirror
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from draftgeoutils.general import geomType, edg, vec, NORM, v1
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from draftgeoutils.geometry import mirror, findDistance
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from draftgeoutils.edges import findMidpoint
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from draftgeoutils.intersections import findIntersection, angleBisection
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@@ -176,3 +176,318 @@ def circleFrom2LinesRadius(edge1, edge2, radius):
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circles.append(Part.Circle(cen, NORM, radius))
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return circles
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def circleFrom3LineTangents(edge1, edge2, edge3):
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"""Return a list of circles from three edges.
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It calculates up to 6 possible centers.
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"""
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def rot(ed):
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geo = Part.LineSegment(v1(ed),
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v1(ed).add(DraftVecUtils.rotate(vec(ed),
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math.pi/2)))
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return geo.toShape()
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bis12 = angleBisection(edge1, edge2)
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bis23 = angleBisection(edge2, edge3)
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bis31 = angleBisection(edge3, edge1)
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intersections = []
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intsec = findIntersection(bis12, bis23, True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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intsec = findIntersection(bis23, bis31, True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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intsec = findIntersection(bis31, bis12, True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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intsec = findIntersection(rot(bis12), rot(bis23), True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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intsec = findIntersection(rot(bis23), rot(bis31), True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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intsec = findIntersection(rot(bis31), rot(bis12), True, True)
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if intsec:
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radius = findDistance(intsec[0], edge1).Length
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intersections.append(Part.Circle(intsec[0], NORM, radius))
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circles = []
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for intsec in intersections:
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exists = False
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for cir in circles:
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if DraftVecUtils.equals(cir.Center, intsec.Center):
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exists = True
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break
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if not exists:
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circles.append(intsec)
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if circles:
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return circles
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else:
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return None
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def circleFromPointLineRadius(point, edge, radius):
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"""Return a list of circles from one point, one edge, and one radius.
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It calculates up to 2 possible centers.
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"""
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dist = findDistance(point, edge, False)
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center1 = None
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center2 = None
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if dist.Length == 0:
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segment = vec(edge)
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perpVec = DraftVecUtils.crossproduct(segment)
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perpVec.normalize()
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normPoint_c1 = App.Vector(perpVec).multiply(radius)
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normPoint_c2 = App.Vector(perpVec).multiply(-radius)
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center1 = point.add(normPoint_c1)
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center2 = point.add(normPoint_c2)
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elif dist.Length > 2 * radius:
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return None
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elif dist.Length == 2 * radius:
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normPoint = point.add(findDistance(point, edge, False))
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dummy = (normPoint.sub(point)).multiply(0.5)
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cen = point.add(dummy)
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circ = Part.Circle(cen, NORM, radius)
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if circ:
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return [circ]
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else:
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return None
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else:
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normPoint = point.add(findDistance(point, edge, False))
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normDist = DraftVecUtils.dist(normPoint, point)
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dist = math.sqrt(radius**2 - (radius - normDist)**2)
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centerNormVec = DraftVecUtils.scaleTo(point.sub(normPoint), radius)
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edgeDir = edge.Vertexes[0].Point.sub(normPoint)
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edgeDir.normalize()
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center1 = centerNormVec.add(normPoint.add(App.Vector(edgeDir).multiply(dist)))
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center2 = centerNormVec.add(normPoint.add(App.Vector(edgeDir).multiply(-dist)))
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circles = []
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if center1:
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circ = Part.Circle(center1, NORM, radius)
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if circ:
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circles.append(circ)
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if center2:
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circ = Part.Circle(center2, NORM, radius)
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if circ:
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circles.append(circ)
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if circles:
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return circles
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else:
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return None
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def circleFrom2PointsRadius(p1, p2, radius):
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"""Return a list of circles from two points, and one radius.
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The two points must not be equal.
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It calculates up to 2 possible centers.
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"""
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if DraftVecUtils.equals(p1, p2):
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return None
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p1_p2 = Part.LineSegment(p1, p2).toShape()
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dist_p1p2 = DraftVecUtils.dist(p1, p1)
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mid = findMidpoint(p1_p2)
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if dist_p1p2 == 2*radius:
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circle = Part.Circle(mid, NORM, radius)
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if circle:
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return [circle]
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else:
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return None
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_dir = vec(p1_p2)
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_dir.normalize()
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perpDir = _dir.cross(App.Vector(0, 0, 1))
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perpDir.normalize()
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dist = math.sqrt(radius**2 - (dist_p1p2 / 2.0)**2)
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cen1 = App.Vector.add(mid, App.Vector(perpDir).multiply(dist))
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cen2 = App.Vector.add(mid, App.Vector(perpDir).multiply(-dist))
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circles = []
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if cen1:
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circles.append(Part.Circle(cen1, NORM, radius))
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if cen2:
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circles.append(Part.Circle(cen2, NORM, radius))
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if circles:
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return circles
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else:
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return None
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def findHomotheticCenterOfCircles(circle1, circle2):
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"""Calculate the homothetic centers from two circles.
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Return None if the objects are not circles, or if they are concentric.
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http://en.wikipedia.org/wiki/Homothetic_center
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http://mathworld.wolfram.com/HomotheticCenter.html
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"""
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if (geomType(circle1) == "Circle" and geomType(circle2) == "Circle"):
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print("debug: findHomotheticCenterOfCircles bad parameters!")
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return None
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if DraftVecUtils.equals(circle1.Curve.Center,
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circle2.Curve.Center):
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return None
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|
||||
cen1_cen2 = Part.LineSegment(circle1.Curve.Center,
|
||||
circle2.Curve.Center).toShape()
|
||||
cenDir = vec(cen1_cen2)
|
||||
cenDir.normalize()
|
||||
|
||||
# Get the perpedicular vector.
|
||||
perpCenDir = cenDir.cross(App.Vector(0, 0, 1))
|
||||
perpCenDir.normalize()
|
||||
|
||||
# Get point on first circle
|
||||
p1 = App.Vector.add(circle1.Curve.Center,
|
||||
App.Vector(perpCenDir).multiply(circle1.Curve.Radius))
|
||||
|
||||
centers = []
|
||||
# Calculate inner homothetic center
|
||||
# Get point on second circle
|
||||
p2_inner = App.Vector.add(circle1.Curve.Center,
|
||||
App.Vector(perpCenDir).multiply(-circle1.Curve.Radius))
|
||||
hCenterInner = DraftVecUtils.intersect(circle1.Curve.Center,
|
||||
circle2.Curve.Center,
|
||||
p1, p2_inner,
|
||||
True, True)
|
||||
if hCenterInner:
|
||||
centers.append(hCenterInner)
|
||||
|
||||
# Calculate outer homothetic center; it only exists if the circles
|
||||
# have different radii
|
||||
if circle1.Curve.Radius != circle2.Curve.Radius:
|
||||
# Get point on second circle
|
||||
p2_outer = App.Vector.add(circle1.Curve.Center,
|
||||
App.Vector(perpCenDir).multiply(circle1.Curve.Radius))
|
||||
hCenterOuter = DraftVecUtils.intersect(circle1.Curve.Center,
|
||||
circle2.Curve.Center,
|
||||
p1, p2_outer,
|
||||
True, True)
|
||||
if hCenterOuter:
|
||||
centers.append(hCenterOuter)
|
||||
|
||||
if centers:
|
||||
return centers
|
||||
else:
|
||||
return None
|
||||
|
||||
|
||||
def findRadicalAxis(circle1, circle2):
|
||||
"""Calculate the radical axis of two circles.
|
||||
|
||||
On the radical axis (also called power line) of two circles any
|
||||
tangents drawn from a point on the axis to both circles have
|
||||
the same length.
|
||||
|
||||
http://en.wikipedia.org/wiki/Radical_axis
|
||||
http://mathworld.wolfram.com/RadicalLine.html
|
||||
|
||||
See Also
|
||||
--------
|
||||
findRadicalCenter
|
||||
"""
|
||||
if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle"):
|
||||
print("debug: findRadicalAxis bad parameters! Must be circles.")
|
||||
return None
|
||||
|
||||
if DraftVecUtils.equals(circle1.Curve.Center, circle2.Curve.Center):
|
||||
return None
|
||||
|
||||
r1 = circle1.Curve.Radius
|
||||
r2 = circle1.Curve.Radius
|
||||
cen1 = circle1.Curve.Center
|
||||
# dist .. the distance from cen1 to cen2.
|
||||
dist = DraftVecUtils.dist(cen1, circle2.Curve.Center)
|
||||
cenDir = cen1.sub(circle2.Curve.Center)
|
||||
cenDir.normalize()
|
||||
|
||||
# Get the perpedicular vector.
|
||||
perpCenDir = cenDir.cross(App.Vector(0, 0, 1))
|
||||
perpCenDir.normalize()
|
||||
|
||||
# J ... The radical center.
|
||||
# K ... The point where the cadical axis crosses the line of cen1->cen2.
|
||||
# k1 ... Distance from cen1 to K.
|
||||
# k2 ... Distance from cen2 to K.
|
||||
# dist = k1 + k2
|
||||
|
||||
k1 = (dist + (r1**2 - r2**2) / dist) / 2.0
|
||||
# k2 = dist - k1
|
||||
|
||||
K = App.Vector.add(cen1, cenDir.multiply(k1))
|
||||
|
||||
# K_ .. A point somewhere between K and J; actually with a distance
|
||||
# of 1 unit from K.
|
||||
K_ = App.Vector.add(K, perpCenDir)
|
||||
|
||||
# Original code didn't specify the value of origin nor dir,
|
||||
# so this is a guess:
|
||||
# radicalAxis = Part.LineSegment(K, Vector.add(origin, dir))
|
||||
|
||||
origin = App.Vector(0, 0, 0)
|
||||
radicalAxis = Part.LineSegment(K, App.Vector.add(origin, perpCenDir))
|
||||
|
||||
if radicalAxis:
|
||||
return radicalAxis
|
||||
else:
|
||||
return None
|
||||
|
||||
|
||||
def findRadicalCenter(circle1, circle2, circle3):
|
||||
"""Calculate the radical center of three circles.
|
||||
|
||||
It is also called the power center.
|
||||
It is the intersection point of the three radical axes of the pairs
|
||||
of circles.
|
||||
|
||||
http://en.wikipedia.org/wiki/Power_center_(geometry)
|
||||
http://mathworld.wolfram.com/RadicalCenter.html
|
||||
|
||||
See Also
|
||||
--------
|
||||
findRadicalAxis
|
||||
"""
|
||||
if (geomType(circle1) != "Circle"
|
||||
or geomType(circle2) != "Circle"
|
||||
or geomType(circle3) != "Circle"):
|
||||
print("debug: findRadicalCenter bad parameters! Must be circles.")
|
||||
return None
|
||||
|
||||
radicalAxis12 = findRadicalAxis(circle1, circle2)
|
||||
radicalAxis23 = findRadicalAxis(circle2, circle3)
|
||||
|
||||
if not radicalAxis12 or not radicalAxis23:
|
||||
# No radical center could be calculated.
|
||||
return None
|
||||
|
||||
intersect = findIntersection(radicalAxis12, radicalAxis23, True, True)
|
||||
|
||||
if intersect:
|
||||
return intersect
|
||||
else:
|
||||
# No radical center could be calculated.
|
||||
return None
|
||||
|
||||
Reference in New Issue
Block a user