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152 lines
4.5 KiB
ReStructuredText
152 lines
4.5 KiB
ReStructuredText
.. _location_arithmetics:
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Location arithmetic for algebra mode
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======================================
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Position a shape relative to the XY plane
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---------------------------------------------
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For the following use the helper function:
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.. code-block:: python
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def location_symbol(location: Location, scale: float = 1) -> Compound:
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return Compound.make_triad(axes_scale=scale).locate(location)
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def plane_symbol(plane: Plane, scale: float = 1) -> Compound:
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triad = Compound.make_triad(axes_scale=scale)
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circle = Circle(scale * .8).edge()
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return (triad + circle).locate(plane.location)
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1. **Positioning at a location**
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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.. image:: assets/location-example-01.png
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2) **Positioning on a plane**
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.. code-block:: python
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plane = Plane.XZ
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face = plane * Rectangle(1, 2)
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show_object(face, name="face")
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show_object(plane_symbol(plane), name="plane")
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.. image:: assets/location-example-07.png
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Note that the ``x``-axis and the ``y``-axis of the plane are on the ``x``-axis and the ``z``-axis of the world coordinate system (red and blue axis)
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Relative positioning to a plane
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------------------------------------
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1. **Position an object on a plane relative to the plane**
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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box = Plane(loc) * Pos(0.2, 0.4, 0.1) * Box(0.2, 0.2, 0.2)
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# box = Plane(face.location) * Pos(0.2, 0.4, 0.1) * Box(0.2, 0.2, 0.2)
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# box = loc * Pos(0.2, 0.4, 0.1) * Box(0.2, 0.2, 0.2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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show_object(box, name="box")
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.. image:: assets/location-example-02.png
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The ``x``, ``y``, ``z`` components of ``Pos(0.2, 0.4, 0.1)`` are relative to the ``x``-axis, ``y``-axis or
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``z``-axis of the underlying location ``loc``.
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Note: ``Plane(loc) *``, ``Plane(face.location) *`` and ``loc *`` are equivalent in this example.
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2. **Rotate an object on a plane relative to the plane**
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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box = Plane(loc) * Rot(z=80) * Box(0.2, 0.2, 0.2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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show_object(box, name="box")
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.. image:: assets/location-example-03.png
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The box is rotated via ``Rot(z=80)`` around the ``z``-axis of the underlying location
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(and not of the z-axis of the world).
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More general:
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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box = loc * Rot(20, 40, 80) * Box(0.2, 0.2, 0.2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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show_object(box, name="box")
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.. image:: assets/location-example-04.png
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The box is rotated via ``Rot(20, 40, 80)`` around all three axes relative to the plane.
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3. **Rotate and position an object relative to a location**
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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box = loc * Rot(20, 40, 80) * Pos(0.2, 0.4, 0.1) * Box(0.2, 0.2, 0.2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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show_object(box, name="box")
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show_object(location_symbol(loc * Rot(20, 40, 80), 0.5), options={"color":(0, 255, 255)}, name="local_location")
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.. image:: assets/location-example-05.png
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The box is positioned via ``Pos(0.2, 0.4, 0.1)`` relative to the location ``loc * Rot(20, 40, 80)``
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4. **Position and rotate an object relative to a location**
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.. code-block:: python
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loc = Location((0.1, 0.2, 0.3), (10, 20, 30))
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face = loc * Rectangle(1,2)
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box = loc * Pos(0.2, 0.4, 0.1) * Rot(20, 40, 80) * Box(0.2, 0.2, 0.2)
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show_object(face, name="face")
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show_object(location_symbol(loc), name="location")
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show_object(box, name="box")
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show_object(location_symbol(loc * Pos(0.2, 0.4, 0.1), 0.5), options={"color":(0, 255, 255)}, name="local_location")
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.. image:: assets/location-example-06.png
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Note: This is the same as `box = loc * Location((0.2, 0.4, 0.1), (20, 40, 80)) * Box(0.2, 0.2, 0.2)`
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