Draft: WorkingPlane, Pythonic style, improved the docstrings, in particular offsetToPoint(); I have some doubts about the implementation in 3D space as it seems to calculate a projected distance, and not the real distance; I don't think this is very helpful when the direction is different from perpendicular (normal); perpendicular distance is certainly the most common case, so I don't know if there is any problem at all in practice.
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vocx-fc
@@ -61,7 +61,8 @@ class plane:
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A vector that is supposed to be perpendicular to `u` and `v`;
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it is helpful although redundant.
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position : Base::Vector3
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A vector that helps define the working plane.
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A point throught which the plane goes through,
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that helps define the working plane.
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stored : bool
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A placeholder for a stored state.
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"""
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@@ -82,7 +83,7 @@ class plane:
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it is redundant.
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It defaults to `(0, 0, 1)`, or the +Z axis.
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pos : Base::Vector3, optional
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The position of the working plane.
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A point through which the plane goes through.
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It defaults to the origin `(0, 0, 0)`.
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"""
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# keep track of active document. Reset view when doc changes.
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@@ -96,40 +97,107 @@ class plane:
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self.stored = None
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def __repr__(self):
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"""Show the string representation of the object."""
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return "Workplane x="+str(DraftVecUtils.rounded(self.u))+" y="+str(DraftVecUtils.rounded(self.v))+" z="+str(DraftVecUtils.rounded(self.axis))
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def copy(self):
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"""Return a new plane that is a copy of the present object."""
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return plane(u=self.u, v=self.v, w=self.axis, pos=self.position)
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def offsetToPoint(self, p, direction=None):
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'''
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Return the signed distance from p to the plane, such
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that p + offsetToPoint(p)*direction lies on the plane.
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direction defaults to -plane.axis
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'''
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"""Return the signed distance from a point to the plane.
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'''
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A picture will help explain the computation:
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Parameters
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----------
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p : Base::Vector3
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The external point to consider.
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direction : Base::Vector3, optional
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The unit vector that indicates the direction of the distance.
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p
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//|
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/ / |
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/ / |
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/ / |
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/ / |
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-------------------- plane -----c-----x-----a--------
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It defaults to `None`, which then uses the `plane.axis` (normal)
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value, meaning that the measured distance is perpendicular
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to the plane.
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Here p is the specified point,
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c is a point (in this case plane.position) on the plane
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x is the intercept on the plane from p in the specified direction, and
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a is the perpendicular intercept on the plane (i.e. along plane.axis)
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Returns
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-------
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float
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The distance from the point to the plane.
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Using vertival bars to denote the length operator,
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|ap| = |cp| * cos(apc) = |xp| * cos(apx)
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so
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|xp| = |cp| * cos(apc) / cos(apx)
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= (cp . axis) / (direction . axis)
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'''
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Notes
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-----
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The signed distance `d`, from `p` to the plane, is such that
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::
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x = p + d*direction,
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where `x` is a point that lies on the plane.
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The `direction` is a unit vector that specifies the direction
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in which the distance is measured.
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It defaults to `plane.axis`,
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meaning that it is the perpendicular distance.
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A picture will help explain the computation
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::
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p
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//|
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/ / |
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d / / | axis
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/ / |
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/ / |
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-------- plane -----x-----c-----a--------
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The points are as follows
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* `p` is an arbitraty point outside the plane.
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* `c` is a known point on the plane,
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for example, `plane.position`.
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* `x` is the intercept on the plane from `p` in
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the desired `direction`.
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* `a` is the perpendicular intercept on the plane,
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i.e. along `plane.axis`.
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The distance is calculated through the dot product
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of the vector `pc` (going from point `p` to point `c`,
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both of which are known) with the unit vector `direction`
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(which is provided or defaults to `plane.axis`).
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::
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d = pc . direction
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d = (c - p) . direction
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**Warning:** this implementation doesn't calculate the entire
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distance `|xp|`, only the distance `|pc|` projected onto `|xp|`.
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Trigonometric relationships
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---------------------------
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In 2D the distances can be calculated by trigonometric relationships
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::
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|ap| = |cp| cos(apc) = |xp| cos(apx)
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Then the desired distance is `d = |xp|`
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::
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|xp| = |cp| cos(apc) / cos(apx)
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The cosines can be obtained from the definition of the dot product
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::
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A . B = |A||B| cos(angleAB)
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If one vector is a unit vector
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::
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A . uB = |A| cos(angleAB)
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cp . axis = |cp| cos(apc)
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and if both vectors are unit vectors
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::
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uA . uB = cos(angleAB).
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direction . axis = cos(apx)
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Then
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::
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d = (cp . axis) / (direction . axis)
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**Note:** for 2D these trigonometric operations
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produce the full `|xp|` distance.
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"""
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if direction == None: direction = self.axis
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return direction.dot(self.position.sub(p))
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