# *************************************************************************** # * Copyright (c) 2009, 2010 Ken Cline * # * * # * This program is free software; you can redistribute it and/or modify * # * it under the terms of the GNU Lesser General Public License (LGPL) * # * as published by the Free Software Foundation; either version 2 of * # * the License, or (at your option) any later version. * # * for detail see the LICENCE text file. * # * * # * This program 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 Library General Public License for more details. * # * * # * You should have received a copy of the GNU Library General Public * # * License along with this program; if not, write to the Free Software * # * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 * # * USA * # * * # *************************************************************************** """Provide the working plane code and utilities for the Draft Workbench. This module provides the plane class which provides a virtual working plane in FreeCAD and a couple of utility functions. The working plane is mostly intended to be used in the Draft Workbench to draw 2D objects in various orientations, not only in the standard XY, YZ, and XZ planes. """ ## @package WorkingPlane # \ingroup DRAFT # \brief This module handles the Working Plane and grid of the Draft module. # # This module provides the plane class which provides a virtual working plane # in FreeCAD and a couple of utility functions. import math from sys import float_info import lazy_loader.lazy_loader as lz import FreeCAD import DraftVecUtils from FreeCAD import Vector from draftutils.translate import translate DraftGeomUtils = lz.LazyLoader("DraftGeomUtils", globals(), "DraftGeomUtils") Part = lz.LazyLoader("Part", globals(), "Part") FreeCADGui = lz.LazyLoader("FreeCADGui", globals(), "FreeCADGui") __title__ = "FreeCAD Working Plane utility" __author__ = "Ken Cline" __url__ = "https://www.freecad.org" class Plane: """A WorkPlane object. Parameters ---------- u: Base::Vector3, optional An axis (vector) that helps define the working plane. It defaults to `(1, 0, 0)`, or the +X axis. v: Base::Vector3, optional An axis (vector) that helps define the working plane. It defaults to `(0, 1, 0)`, or the +Y axis. w: Base::Vector3, optional An axis that is supposed to be perpendicular to `u` and `v`; it is redundant. It defaults to `(0, 0, 1)`, or the +Z axis. pos: Base::Vector3, optional A point through which the plane goes through. It defaults to the origin `(0, 0, 0)`. Attributes ---------- doc: App::Document The active document. Reset view when `doc` changes. weak: bool It is `True` if the plane has been defined by `setup()` or has been reset. A weak plane can be changed (it is the "auto" mode), while a strong plane will keep its position until weakened (it is "locked") u: Base::Vector3 An axis (vector) that helps define the working plane. v: Base::Vector3 An axis (vector) that helps define the working plane. axis: Base::Vector3 A vector that is supposed to be perpendicular to `u` and `v`; it is helpful although redundant. position: Base::Vector3 A point, which the plane goes through, that helps define the working plane. stored: bool A placeholder for a stored state. """ def __init__(self, u=Vector(1, 0, 0), v=Vector(0, 1, 0), w=Vector(0, 0, 1), pos=Vector(0, 0, 0)): # keep track of active document. Reset view when doc changes. self.doc = None self.weak = True self.u = u self.v = v self.axis = w self.position = pos # a placeholder for a stored state self.stored = None def __repr__(self): """Show the string representation of the object.""" text = "Workplane" text += " x=" + str(DraftVecUtils.rounded(self.u)) text += " y=" + str(DraftVecUtils.rounded(self.v)) text += " z=" + str(DraftVecUtils.rounded(self.axis)) return text def copy(self): """Return a new plane that is a copy of the present object.""" p = plane(u=self.u, v=self.v, w=self.axis, pos=self.position) p.weak = self.weak return p def offsetToPoint(self, p, direction=None): """Return the signed distance from a point to the plane. Parameters ---------- p : Base::Vector3 The external point to consider. direction : Base::Vector3, optional The unit vector that indicates the direction of the distance. It defaults to `None`, which then uses the `plane.axis` (normal) value, meaning that the measured distance is perpendicular to the plane. Returns ------- float The distance from the point to the plane. Notes ----- The signed distance `d`, from `p` to the plane, is such that :: x = p + d*direction, where `x` is a point that lies on the plane. The `direction` is a unit vector that specifies the direction in which the distance is measured. It defaults to `plane.axis`, meaning that it is the perpendicular distance. A picture will help explain the computation :: p //| / / | d / / | axis / / | / / | -------- plane -----x-----c-----a-------- The points are as follows * `p` is an arbitrary point outside the plane. * `c` is a known point on the plane, for example, `plane.position`. * `x` is the intercept on the plane from `p` in the desired `direction`. * `a` is the perpendicular intercept on the plane, i.e. along `plane.axis`. The distance is calculated through the dot product of the vector `pc` (going from point `p` to point `c`, both of which are known) with the unit vector `direction` (which is provided or defaults to `plane.axis`). :: d = pc . direction d = (c - p) . direction **Warning:** this implementation doesn't calculate the entire distance `|xp|`, only the distance `|pc|` projected onto `|xp|`. Trigonometric relationships --------------------------- In 2D the distances can be calculated by trigonometric relationships :: |ap| = |cp| cos(apc) = |xp| cos(apx) Then the desired distance is `d = |xp|` :: |xp| = |cp| cos(apc) / cos(apx) The cosines can be obtained from the definition of the dot product :: A . B = |A||B| cos(angleAB) If one vector is a unit vector :: A . uB = |A| cos(angleAB) cp . axis = |cp| cos(apc) and if both vectors are unit vectors :: uA . uB = cos(angleAB). direction . axis = cos(apx) Then :: d = (cp . axis) / (direction . axis) **Note:** for 2D these trigonometric operations produce the full `|xp|` distance. """ if direction is None: direction = self.axis return direction.dot(self.position.sub(p)) def projectPoint(self, p, direction=None, force_projection=True): """Project a point onto the plane, by default orthogonally. Parameters ---------- p : Base::Vector3 The point to project. direction : Base::Vector3, optional The unit vector that indicates the direction of projection. It defaults to `None`, which then uses the `plane.axis` (normal) value, meaning that the point is projected perpendicularly to the plane. force_projection: Bool, optional Forces the projection if the deviation between the direction and the normal is less than float epsilon from the orthogonality. The direction of projection is modified to a float epsilon deviation between the direction and the orthogonal. It defaults to True. Returns ------- Base::Vector3 The projected vector, scaled to the appropriate distance. """ axis = Vector(self.axis).normalize() if direction is None: dir = axis else: dir = Vector(direction).normalize() cos = dir.dot(axis) delta_ax_proj = (p - self.position).dot(axis) # check the only conflicting case: direction orthogonal to axis if abs(cos) <= float_info.epsilon: if force_projection: cos = math.copysign(float_info.epsilon, delta_ax_proj) dir = axis.cross(dir).cross(axis) - cos*axis else: return None proj = p - delta_ax_proj/cos*dir return proj def projectPointOld(self, p, direction=None): """Project a point onto the plane. OBSOLETE. Parameters ---------- p : Base::Vector3 The point to project. direction : Base::Vector3, optional The unit vector that indicates the direction of projection. It defaults to `None`, which then uses the `plane.axis` (normal) value, meaning that the point is projected perpendicularly to the plane. Returns ------- Base::Vector3 The projected point, or the original point if the angle between the `direction` and the `plane.axis` is 90 degrees. """ if not direction: direction = self.axis t = Vector(direction) # t.normalize() a = round(t.getAngle(self.axis), DraftVecUtils.precision()) pp = round((math.pi)/2, DraftVecUtils.precision()) if a == pp: return p t.multiply(self.offsetToPoint(p, direction)) return p.add(t) def alignToPointAndAxis(self, point, axis, offset=0, upvec=None): """Align the working plane to a point and an axis (vector). Set `v` as the cross product of `axis` with `(1, 0, 0)` or `+X`, and `u` as `v` rotated -90 degrees around the `axis`. Also set `weak` to `False`. Parameters ---------- point : Base::Vector3 The new `position` of the plane, adjusted by the `offset`. axis : Base::Vector3 A vector whose unit vector will be used as the new `axis` of the plane. If it is very close to the `X` or `-X` axes, it will use this axis exactly, and will adjust `u` and `v` to `+Y` and `+Z`, or `-Y` and `+Z`, respectively. offset : float, optional Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. upvec : Base::Vector3, optional Defaults to `None`. If it exists, its unit vector will be used as `v`, and will set `u` as the cross product of `v` with `axis`. """ self.doc = FreeCAD.ActiveDocument self.axis = axis self.axis.normalize() if axis.getAngle(Vector(1, 0, 0)) < 0.00001: self.axis = Vector(1, 0, 0) self.u = Vector(0, 1, 0) self.v = Vector(0, 0, 1) elif axis.getAngle(Vector(-1, 0, 0)) < 0.00001: self.axis = Vector(-1, 0, 0) self.u = Vector(0, -1, 0) self.v = Vector(0, 0, 1) elif upvec: self.u = upvec.cross(self.axis) self.u.normalize() self.v = self.axis.cross(self.u) self.v.normalize() else: self.v = axis.cross(Vector(1, 0, 0)) self.v.normalize() self.u = DraftVecUtils.rotate(self.v, -math.pi/2, self.axis) self.u.normalize() offsetVector = Vector(axis) offsetVector.multiply(offset) self.position = point.add(offsetVector) self.weak = False # Console.PrintMessage("(position = " + str(self.position) + ")\n") # Console.PrintMessage(self.__repr__() + "\n") def alignToPointAndAxis_SVG(self, point, axis, offset=0): """Align the working plane to a point and an axis (vector). It aligns `u` and `v` based on the magnitude of the components of `axis`. Also set `weak` to `False`. Parameters ---------- point : Base::Vector3 The new `position` of the plane, adjusted by the `offset`. axis : Base::Vector3 A vector whose unit vector will be used as the new `axis` of the plane. The magnitudes of the `x`, `y`, `z` components of the axis determine the orientation of `u` and `v` of the plane. offset : float, optional Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. Cases ----- The `u` and `v` are always calculated the same * `u` is the cross product of the positive or negative of `axis` with a `reference vector`. :: u = [+1|-1] axis.cross(ref_vec) * `v` is `u` rotated 90 degrees around `axis`. Whether the `axis` is positive or negative, and which reference vector is used, depends on the absolute values of the `x`, `y`, `z` components of the `axis` unit vector. #. If `x > y`, and `y > z` The reference vector is +Z :: u = -1 axis.cross(+Z) #. If `y > z`, and `z >= x` The reference vector is +X. :: u = -1 axis.cross(+X) #. If `y >= x`, and `x > z` The reference vector is +Z. :: u = +1 axis.cross(+Z) #. If `x > z`, and `z >= y` The reference vector is +Y. :: u = +1 axis.cross(+Y) #. If `z >= y`, and `y > x` The reference vector is +X. :: u = +1 axis.cross(+X) #. otherwise The reference vector is +Y. :: u = -1 axis.cross(+Y) """ self.doc = FreeCAD.ActiveDocument self.axis = axis self.axis.normalize() ref_vec = Vector(0.0, 1.0, 0.0) if ((abs(axis.x) > abs(axis.y)) and (abs(axis.y) > abs(axis.z))): ref_vec = Vector(0.0, 0., 1.0) self.u = axis.negative().cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "Case new" elif ((abs(axis.y) > abs(axis.z)) and (abs(axis.z) >= abs(axis.x))): ref_vec = Vector(1.0, 0.0, 0.0) self.u = axis.negative().cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "Y>Z, View Y" elif ((abs(axis.y) >= abs(axis.x)) and (abs(axis.x) > abs(axis.z))): ref_vec = Vector(0.0, 0., 1.0) self.u = axis.cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "ehem. XY, Case XY" elif ((abs(axis.x) > abs(axis.z)) and (abs(axis.z) >= abs(axis.y))): self.u = axis.cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "X>Z, View X" elif ((abs(axis.z) >= abs(axis.y)) and (abs(axis.y) > abs(axis.x))): ref_vec = Vector(1.0, 0., 0.0) self.u = axis.cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "Y>X, Case YZ" else: self.u = axis.negative().cross(ref_vec) self.u.normalize() self.v = DraftVecUtils.rotate(self.u, math.pi/2, self.axis) # projcase = "else" # spat_vec = self.u.cross(self.v) # spat_res = spat_vec.dot(axis) # Console.PrintMessage(projcase + " spat Prod = " + str(spat_res) + "\n") offsetVector = Vector(axis) offsetVector.multiply(offset) self.position = point.add(offsetVector) self.weak = False # Console.PrintMessage("(position = " + str(self.position) + ")\n") # Console.PrintMessage(self.__repr__() + "\n") def alignToCurve(self, shape, offset=0): """Align plane to curve. NOT YET IMPLEMENTED. Parameters ---------- shape : Part.Shape A curve that will serve to align the plane. It can be an `'Edge'` or `'Wire'`. offset : float Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. Returns ------- False Returns `False` if the shape is null. Currently it always returns `False`. """ if shape.isNull(): return False elif shape.ShapeType == 'Edge': # ??? TODO: process curve here. look at shape.edges[0].Curve return False elif shape.ShapeType == 'Wire': # ??? TODO: determine if edges define a plane return False else: return False def alignToEdges(self, edges): """Align plane to two edges. Uses the two points of the first edge to define the direction of the unit vector `u`, the other two points of the other edge to define the other unit vector `v`, and then the cross product of `u` with `v` to define the `axis`. Parameters ---------- edges : list A list of two edges. Returns ------- False Return `False` if `edges` is a list of more than 2 elements. """ # use a list of edges to find a plane position if len(edges) > 2: return False # for axes systems, we suppose the 2 first edges are parallel # ??? TODO: exclude other cases first v1 = edges[0].Vertexes[-1].Point.sub(edges[0].Vertexes[0].Point) v2 = edges[1].Vertexes[0].Point.sub(edges[0].Vertexes[0].Point) v3 = v1.cross(v2) v1.normalize() v2.normalize() v3.normalize() # print(v1,v2,v3) self.u = v1 self.v = v2 self.axis = v3 def alignToFace(self, shape, offset=0, parent=None): """Align the plane to a face. It uses the center of mass of the face as `position`, and its normal in the center of the face as `axis`, then calls `alignToPointAndAxis(position, axis, offset)`. If the face is a quadrilateral, then it adjusts the position of the plane according to its reported X direction and Y direction. Also set `weak` to `False`. Parameter -------- shape : Part.Face A shape of type `'Face'`. offset : float Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. parent : object Defaults to None. The ParentGeoFeatureGroup of the object the face belongs to. Returns ------- bool `True` if the operation was successful, and `False` if the shape is not a `'Face'`. See Also -------- alignToPointAndAxis """ # Set face to the unique selected face, if found if shape.ShapeType == 'Face': if parent: place = parent.getGlobalPlacement() else: place = FreeCAD.Placement() rot = place.Rotation cen = place.multVec(shape.CenterOfMass) nor = rot.multVec(shape.normalAt(0, 0)) self.alignToPointAndAxis(cen, nor, offset) pmr = shape.ParameterRange # (uMin, uMax, vMin, vMax) u = shape.valueAt(pmr[1], 0).sub(shape.valueAt(pmr[0], 0)) v = shape.valueAt(0, pmr[3]).sub(shape.valueAt(0, pmr[2])) self.u = rot.multVec(u).normalize() self.v = rot.multVec(v).normalize() if shape.Orientation == "Reversed": self.u, self.v = self.v, self.u # If self.u or self.v matches a wrong global axis, rotate them: if DraftVecUtils.equals(self.v, Vector(0, 0, -1)): self.u, self.v = self.u.negative(), self.v.negative() elif DraftVecUtils.equals(self.u, Vector(0, 0, 1)): self.u, self.v = self.v.negative(), self.u elif DraftVecUtils.equals(self.u, Vector(0, 0, -1)): self.u, self.v = self.v, self.u.negative() self.weak = False return True else: return False def alignTo3Points(self, p1, p2, p3, offset=0): """Align the plane to three points. It makes a closed quadrilateral face with the three points, and then calls `alignToFace(shape, offset)`. Parameter --------- p1 : Base::Vector3 The first point. p2 : Base::Vector3 The second point. p3 : Base::Vector3 The third point. offset : float Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. Returns ------- bool `True` if the operation was successful, and `False` otherwise. """ import Part w = Part.makePolygon([p1, p2, p3, p1]) f = Part.Face(w) return self.alignToFace(f, offset) def alignToSelection(self, offset=0): """Align the plane to a selection if it defines a plane. If the selection uniquely defines a plane it will be used. Parameter --------- offset : float Defaults to zero. A value which will be used to offset the plane in the direction of its `axis`. Returns ------- bool `True` if the operation was successful, and `False` otherwise. It returns `False` if the selection has no elements, or if the object is not derived from `'Part::Feature'` or if the object doesn't have a `Shape`. See Also -------- alignToFace, alignToCurve """ sel_ex = FreeCADGui.Selection.getSelectionEx(FreeCAD.ActiveDocument.Name) if not sel_ex: return False shapes = list() names = list() for obj in sel_ex: # check that the geometric property is a Part.Shape object geom_is_shape = False if isinstance(obj.Object, FreeCAD.GeoFeature): geom = obj.Object.getPropertyOfGeometry() if isinstance(geom, Part.Shape): geom_is_shape = True if not geom_is_shape: FreeCAD.Console.PrintError(translate( "draft", "Object without Part.Shape geometry:'{}'".format( obj.ObjectName)) + "\n") return False if geom.isNull(): FreeCAD.Console.PrintError(translate( "draft", "Object with null Part.Shape geometry:'{}'".format( obj.ObjectName)) + "\n") return False if obj.HasSubObjects: shapes.extend(obj.SubObjects) names.extend([obj.ObjectName + "." + n for n in obj.SubElementNames]) else: shapes.append(geom) names.append(obj.ObjectName) normal = None for n in range(len(shapes)): if not DraftGeomUtils.is_planar(shapes[n]): FreeCAD.Console.PrintError(translate( "draft", "'{}' object is not planar".format(names[n])) + "\n") return False if not normal: normal = DraftGeomUtils.get_normal(shapes[n]) shape_ref = n # test if all shapes are coplanar if normal: for n in range(len(shapes)): if not DraftGeomUtils.are_coplanar(shapes[shape_ref], shapes[n]): FreeCAD.Console.PrintError(translate( "draft", "{} and {} aren't coplanar".format( names[shape_ref],names[n])) + "\n") return False else: # suppose all geometries are straight lines or points points = [vertex.Point for shape in shapes for vertex in shape.Vertexes] if len(points) >= 3: poly = Part.makePolygon(points) if not DraftGeomUtils.is_planar(poly): FreeCAD.Console.PrintError(translate( "draft", "All Shapes must be coplanar") + "\n") return False normal = DraftGeomUtils.get_normal(poly) else: normal = None if not normal: FreeCAD.Console.PrintError(translate( "draft", "Selected Shapes must define a plane") + "\n") return False # set center of mass ctr_mass = FreeCAD.Vector(0,0,0) ctr_pts = FreeCAD.Vector(0,0,0) mass = 0 for shape in shapes: if hasattr(shape, "CenterOfMass"): ctr_mass += shape.CenterOfMass*shape.Mass mass += shape.Mass else: ctr_pts += shape.Point if mass > 0: ctr_mass /= mass # all shapes are vertexes else: ctr_mass = ctr_pts/len(shapes) self.alignToPointAndAxis(ctr_mass, normal, offset) return True def setup(self, direction=None, point=None, upvec=None, force=False): """Set up the working plane if it exists but is undefined. If `direction` and `point` are present, it calls `alignToPointAndAxis(point, direction, 0, upvec)`. Otherwise, it gets the camera orientation to define a working plane that is perpendicular to the current view, centered at the origin, and with `v` pointing up on the screen. This method only works when the `weak` attribute is `True`. This method also sets `weak` to `True`. This method only works when `FreeCAD.GuiUp` is `True`, that is, when the graphical interface is loaded. Otherwise it fails silently. Parameters ---------- direction : Base::Vector3, optional It defaults to `None`. It is the new `axis` of the plane. point : Base::Vector3, optional It defaults to `None`. It is the new `position` of the plane. upvec : Base::Vector3, optional It defaults to `None`. It is the new `v` orientation of the plane. force : Bool If True, it sets the plane even if the plane is not in weak mode To do ----- When the interface is not loaded it should fail and print a message, `FreeCAD.Console.PrintError()`. """ if self.weak or force: if direction and point: self.alignToPointAndAxis(point, direction, 0, upvec) elif FreeCAD.GuiUp: try: import FreeCADGui from pivy import coin view = FreeCADGui.ActiveDocument.ActiveView camera = view.getCameraNode() rot = camera.getField("orientation").getValue() coin_up = coin.SbVec3f(0, 1, 0) upvec = Vector(rot.multVec(coin_up).getValue()) vdir = view.getViewDirection() # don't change the plane if the axis and v vector # are already correct: tol = Part.Precision.angular() if abs(math.pi - vdir.getAngle(self.axis)) > tol \ or abs(math.pi - upvec.getAngle(self.v)) > tol: self.alignToPointAndAxis(Vector(0, 0, 0), vdir.negative(), 0, upvec) except Exception: pass if force: self.weak = False else: self.weak = True def reset(self): """Reset the plane. Set the `doc` attribute to `None`, and `weak` to `True`. """ self.doc = None self.weak = True def setTop(self): """sets the WP to top position and updates the GUI""" self.alignToPointAndAxis(FreeCAD.Vector(0.0, 0.0, 0.0), FreeCAD.Vector(0, 0, 1), 0.0) if FreeCAD.GuiUp: import FreeCADGui from draftutils.translate import translate if hasattr(FreeCADGui,"Snapper"): FreeCADGui.Snapper.setGrid() if hasattr(FreeCADGui,"draftToolBar"): FreeCADGui.draftToolBar.wplabel.setText(translate("draft", "Top")) def setFront(self): """sets the WP to front position and updates the GUI""" self.alignToPointAndAxis(FreeCAD.Vector(0.0, 0.0, 0.0), FreeCAD.Vector(0, 1, 0), 0.0) if FreeCAD.GuiUp: import FreeCADGui from draftutils.translate import translate if hasattr(FreeCADGui,"Snapper"): FreeCADGui.Snapper.setGrid() if hasattr(FreeCADGui,"draftToolBar"): FreeCADGui.draftToolBar.wplabel.setText(translate("draft", "Front")) def setSide(self): """sets the WP to top position and updates the GUI""" self.alignToPointAndAxis(FreeCAD.Vector(0.0, 0.0, 0.0), FreeCAD.Vector(-1, 0, 0), 0.0) if FreeCAD.GuiUp: import FreeCADGui from draftutils.translate import translate if hasattr(FreeCADGui,"Snapper"): FreeCADGui.Snapper.setGrid() if hasattr(FreeCADGui,"draftToolBar"): FreeCADGui.draftToolBar.wplabel.setText(translate("draft", "Side")) def getRotation(self): """Return a placement describing the plane orientation only. If `FreeCAD.GuiUp` is `True`, that is, if the graphical interface is loaded, it will test if the active object is an `Arch` container and will calculate the placement accordingly. Returns ------- Base::Placement A placement, comprised of a `Base` (`Base::Vector3`), and a `Rotation` (`Base::Rotation`). """ m = DraftVecUtils.getPlaneRotation(self.u, self.v) p = FreeCAD.Placement(m) # Arch active container if FreeCAD.GuiUp: import FreeCADGui if FreeCADGui.ActiveDocument: view = FreeCADGui.ActiveDocument.ActiveView if view and hasattr(view,"getActiveOject"): a = view.getActiveObject("Arch") if a: p = a.Placement.inverse().multiply(p) return p def getPlacement(self, rotated=False): """Return the placement of the plane. Parameters ---------- rotated : bool, optional It defaults to `False`. If it is `True`, it switches `axis` with `-v` to produce a rotated placement. Returns ------- Base::Placement A placement, comprised of a `Base` (`Base::Vector3`), and a `Rotation` (`Base::Rotation`). """ if rotated: m = DraftVecUtils.getPlaneRotation(self.u, self.axis) else: m = DraftVecUtils.getPlaneRotation(self.u, self.v) m.move(self.position) p = FreeCAD.Placement(m) # Arch active container if based on App Part # if FreeCAD.GuiUp: # import FreeCADGui # view = FreeCADGui.ActiveDocument.ActiveView # a = view.getActiveObject("Arch") # if a: # p = a.Placement.inverse().multiply(p) return p def getNormal(self): """Return the normal vector of the plane (axis). Returns ------- Base::Vector3 The `axis` attribute of the plane. """ n = self.axis # Arch active container if based on App Part # if FreeCAD.GuiUp: # import FreeCADGui # view = FreeCADGui.ActiveDocument.ActiveView # a = view.getActiveObject("Arch") # if a: # n = a.Placement.inverse().Rotation.multVec(n) return n def setFromPlacement(self, pl, rebase=False): """Set the plane from a placement. It normally uses only the rotation, unless `rebase` is `True`. Parameters ---------- pl : Base::Placement or Base::Matrix4D A placement, comprised of a `Base` (`Base::Vector3`), and a `Rotation` (`Base::Rotation`), or a `Base::Matrix4D` that defines a placement. rebase : bool, optional It defaults to `False`. If `True`, it will use `pl.Base` as the new `position` of the plane. Otherwise it will only consider `pl.Rotation`. To do ----- If `pl` is a `Base::Matrix4D`, it shouldn't try to use `pl.Base` because a matrix has no `Base`. """ rot = FreeCAD.Placement(pl).Rotation self.u = rot.multVec(FreeCAD.Vector(1, 0, 0)) self.v = rot.multVec(FreeCAD.Vector(0, 1, 0)) self.axis = rot.multVec(FreeCAD.Vector(0, 0, 1)) if rebase: self.position = pl.Base def inverse(self): """Invert the direction of the plane. It inverts the `u` and `axis` vectors. """ self.u = self.u.negative() self.axis = self.axis.negative() def save(self): """Store the plane attributes. Store `u`, `v`, `axis`, `position` and `weak` in a list in `stored`. """ self.stored = [self.u, self.v, self.axis, self.position, self.weak] def restore(self): """Restore the plane attributes that were saved. Restores the attributes `u`, `v`, `axis`, `position` and `weak` from `stored`, and set `stored` to `None`. """ if self.stored: self.u = self.stored[0] self.v = self.stored[1] self.axis = self.stored[2] self.position = self.stored[3] self.weak = self.stored[4] self.stored = None def getLocalCoords(self, point): """Return the coordinates of the given point, from the plane. If the `point` was constructed using the plane as origin, return the relative coordinates from the `point` to the plane. A vector is calculated from the plane's `position` to the external `point`, and this vector is projected onto each of the `u`, `v` and `axis` of the plane to determine the local, relative vector. Parameters ---------- point : Base::Vector3 The point external to the plane. Returns ------- Base::Vector3 The relative coordinates of the point from the plane. See Also -------- getGlobalCoords, getLocalRot, getGlobalRot Notes ----- The following graphic explains the coordinates. :: g GlobalCoords (1, 11) | | | (n) p point (1, 6) | LocalCoords (1, 1) | ----plane--------c-------- position (0, 5) In the graphic * `p` is an arbitrary point, external to the plane * `c` is the plane's `position` * `g` is the global coordinates of `p` when added to the plane * `n` is the relative coordinates of `p` when referred to the plane To do ----- Maybe a better name would be getRelativeCoords? """ pt = point.sub(self.position) xv = DraftVecUtils.project(pt, self.u) x = xv.Length # If the angle between the projection xv and u # is larger than 1 radian (57.29 degrees), use the negative # of the magnitude. Why exactly 1 radian? if xv.getAngle(self.u) > 1: x = -x yv = DraftVecUtils.project(pt, self.v) y = yv.Length if yv.getAngle(self.v) > 1: y = -y zv = DraftVecUtils.project(pt, self.axis) z = zv.Length if zv.getAngle(self.axis) > 1: z = -z return Vector(x, y, z) def getGlobalCoords(self, point): """Return the coordinates of the given point, added to the plane. If the `point` was constructed using the plane as origin, return the absolute coordinates from the `point` to the global origin. The `u`, `v`, and `axis` vectors scale the components of `point`, and the result is added to the planes `position`. Parameters ---------- point : Base::Vector3 The external point. Returns ------- Base::Vector3 The coordinates of the point from the absolute origin. See Also -------- getLocalCoords, getLocalRot, getGlobalRot Notes ----- The following graphic explains the coordinates. :: g GlobalCoords (1, 11) | | | (n) p point (1, 6) | LocalCoords (1, 1) | ----plane--------c-------- position (0, 5) In the graphic * `p` is an arbitrary point, external to the plane * `c` is the plane's `position` * `g` is the global coordinates of `p` when added to the plane * `n` is the relative coordinates of `p` when referred to the plane """ vx = Vector(self.u).multiply(point.x) vy = Vector(self.v).multiply(point.y) vz = Vector(self.axis).multiply(point.z) pt = (vx.add(vy)).add(vz) return pt.add(self.position) def getLocalRot(self, point): """Like getLocalCoords, but doesn't use the plane's position. If the `point` was constructed using the plane as origin, return the relative coordinates from the `point` to the plane. However, in this case, the plane is assumed to have its `position` at the global origin, therefore, the returned coordinates will only consider the orientation of the plane. The external `point` is a vector, which is projected onto each of the `u`, `v` and `axis` of the plane to determine the local, relative vector. Parameters ---------- point : Base::Vector3 The point external to the plane. Returns ------- Base::Vector3 The relative coordinates of the point from the plane, if the plane had its `position` at the global origin. See Also -------- getLocalCoords, getGlobalCoords, getGlobalRot """ xv = DraftVecUtils.project(point, self.u) x = xv.Length if xv.getAngle(self.u) > 1: x = -x yv = DraftVecUtils.project(point, self.v) y = yv.Length if yv.getAngle(self.v) > 1: y = -y zv = DraftVecUtils.project(point, self.axis) z = zv.Length if zv.getAngle(self.axis) > 1: z = -z return Vector(x, y, z) def getGlobalRot(self, point): """Like getGlobalCoords, but doesn't use the plane's position. If the `point` was constructed using the plane as origin, return the absolute coordinates from the `point` to the global origin. However, in this case, the plane is assumed to have its `position` at the global origin, therefore, the returned coordinates will only consider the orientation of the plane. The `u`, `v`, and `axis` vectors scale the components of `point`. Parameters ---------- point : Base::Vector3 The external point. Returns ------- Base::Vector3 The coordinates of the point from the absolute origin. See Also -------- getGlobalCoords, getLocalCoords, getLocalRot """ vx = Vector(self.u).multiply(point.x) vy = Vector(self.v).multiply(point.y) vz = Vector(self.axis).multiply(point.z) pt = (vx.add(vy)).add(vz) return pt def getClosestAxis(self, point): """Return the closest axis of the plane to the given point (vector). It tests the angle that the `point` vector makes with the unit vectors `u`, `v`, and `axis`, as well their negatives. The smallest angle indicates the closest axis. Parameters ---------- point : Base::Vector3 The external point to test. Returns ------- str * It is `'x'` if the closest axis is `u` or `-u`. * It is `'y'` if the closest axis is `v` or `-v`. * It is `'z'` if the closest axis is `axis` or `-axis`. """ ax = point.getAngle(self.u) ay = point.getAngle(self.v) az = point.getAngle(self.axis) bx = point.getAngle(self.u.negative()) by = point.getAngle(self.v.negative()) bz = point.getAngle(self.axis.negative()) b = min(ax, ay, az, bx, by, bz) if b in [ax, bx]: return "x" elif b in [ay, by]: return "y" elif b in [az, bz]: return "z" else: return None def isGlobal(self): """Return True if the plane axes are equal to the global axes. Return `False` if any of `u`, `v`, or `axis` does not correspond to `+X`, `+Y`, or `+Z`, respectively. """ if self.u != Vector(1, 0, 0): return False if self.v != Vector(0, 1, 0): return False if self.axis != Vector(0, 0, 1): return False return True def isOrtho(self): """Return True if the plane axes are orthogonal with the global axes. Orthogonal means that the angle between `u` and the global axis `+Y` is a multiple of 90 degrees, meaning 0, -90, 90, -180, 180, -270, 270, or 360 degrees. And similarly for `v` and `axis`. All three axes should be orthogonal to the `+Y` axis. Due to rounding errors, the angle difference is rounded to 6 decimal digits to do the test. Returns ------- bool Returns `True` if all three `u`, `v`, and `axis` are orthogonal with the global axis `+Y`. Otherwise it returns `False`. """ ortho = [0, -1.570796, 1.570796, -3.141593, 3.141593, -4.712389, 4.712389, 6.283185] # Shouldn't the angle difference be calculated with # the other global axes `+X` and `+Z` as well? if round(self.u.getAngle(Vector(0, 1, 0)), 6) in ortho: if round(self.v.getAngle(Vector(0, 1, 0)), 6) in ortho: if round(self.axis.getAngle(Vector(0, 1, 0)), 6) in ortho: return True return False def getDeviation(self): """Return the angle between the u axis and the horizontal plane. It defines a projection of `u` on the horizontal plane (without a Z component), and then measures the angle between this projection and `u`. It also considers the cross product of the projection and `u` to determine the sign of the angle. Returns ------- float Angle between the `u` vector, and a projected vector on the global horizontal plane. See Also -------- DraftVecUtils.angle """ proj = Vector(self.u.x, self.u.y, 0) if self.u.getAngle(proj) == 0: return 0 else: norm = proj.cross(self.u) return DraftVecUtils.angle(self.u, proj, norm) def getParameters(self): """Return a dictionary with the data which define the plane: `u`, `v`, `axis`, `weak`. Returns ------- dict dictionary of the form: {"position":position, "u":x, "v":v, "axis":axis, "weak":weak} """ return {"position":self.position, "u":self.u, "v":self.v, "axis":self.axis, "weak":self.weak} def setFromParameters(self, data): """Set the plane according to data. Parameters ---------- data: dict dictionary of the form: {"position":position, "u":x, "v":v, "axis":axis, "weak":weak} """ self.position = data["position"] self.u = data["u"] self.v = data["v"] self.axis = data["axis"] self.weak = data["weak"] return None plane = Plane def getPlacementFromPoints(points): """Return a placement from a list of 3 or 4 points. With these points a temporary `plane` is defined. Then it returns the `Base::Placement` returned from `plane.getPlacement()`. Parameters ---------- points : list of Base::Vector3 A list with 3 or 4 points to create a temporary plane from which to extract the placement. The first point is the plane's `position`. The other two points are used to define the `u` and `v` axes, as originating from the first point. If the fourth point exists, it is used to define the plane's `axis` as originating from the first point. If no fourth point is provided, the cross product bewtween the previously defined `u` and `v` is used as `axis`. Return ------ Base::Placement A placement obtained from the temporary plane defined by `points`, or `None` is it fails to use the points. See Also -------- getPlacement """ pl = plane() try: pl.position = points[0] pl.u = (points[1].sub(points[0]).normalize()) pl.v = (points[2].sub(points[0]).normalize()) if len(points) == 4: pl.axis = (points[3].sub(points[0]).normalize()) else: pl.axis = ((pl.u).cross(pl.v)).normalize() except Exception: return None p = pl.getPlacement() del pl return p def getPlacementFromFace(face, rotated=False): """Return a placement from a face. It creates a temporary `plane` and uses `alignToFace(face)` to set its orientation. Then it returns the `Base::Placement` returned from `plane.getPlacement(rotated)`. Parameter --------- face : Part.Face A shape of type `'Face'`. rotated : bool, optional It defaults to `False`. If it is `True`, the temporary plane switches `axis` with `-v` to produce a rotated placement. Returns ------- Base::Placement A placement obtained from the temporary plane defined by `face`, or `None` if it fails to use `face`. See Also -------- alignToFace, getPlacement """ pl = plane() try: pl.alignToFace(face) except Exception: return None p = pl.getPlacement(rotated) del pl return p