Project
=======

**Method:** ``point.project(angle, distance)``

**Parameters:**

- ``angle`` — bearing direction in **radians** (measured counter-clockwise from the positive :math:`x`-axis)
- ``distance`` — how far to travel along that bearing

**Returns:** ``Point``

----

Description
-----------

``project`` moves a point a given distance along a direction specified as an
angle. Starting from point :math:`P`, the new point :math:`P'` is:

.. math::

   P'_x = P_x + d\cos\theta

.. math::

   P'_y = P_y + d\sin\theta

where :math:`d` is the distance and :math:`\theta` is the angle in radians.

This is equivalent to expressing the displacement in polar coordinates
:math:`(d,\,\theta)` and adding it to the Cartesian position of :math:`P`.

Angle reference
~~~~~~~~~~~~~~~

Angles follow the standard mathematical convention: :math:`0` points along the
positive :math:`x`-axis (east), increasing counter-clockwise.

+---------+-----------------------------------------------------------------+
| Angle   | Direction                                                       |
+=========+=================================================================+
| 0       | East (positive :math:`x`)                                       |
+---------+-----------------------------------------------------------------+
| π / 2   | North (positive :math:`y`)                                      |
+---------+-----------------------------------------------------------------+
| π       | West (negative :math:`x`)                                       |
+---------+-----------------------------------------------------------------+
| 3π / 2  | South (negative :math:`y`)                                      |
+---------+-----------------------------------------------------------------+

Implementation
--------------

.. code-block:: javascript

   project(angle, distance) {
     if (angle === 0) {
       return new Point(this.x, this.y).add(new Point(distance, 0));
     }
     const x = this.x + Math.cos(angle) * distance;
     const y = this.y + Math.sin(angle) * distance;
     return new Point(x, y);
   }

Usage in Design
---------------

``project`` is one of the most widely used geometry helpers in Design-Core:

- **Dimensions** — extension lines and dimension line endpoints are computed
  by projecting measured points along the dimension direction by set offsets.
- **RotatedDimension** — the dimension line direction vector is obtained by
  projecting a unit distance from the first definition point at the user-supplied
  rotation angle, then passing that direction to ``perpendicular()``.
- **Arc generation** — arc vertices are generated by projecting the arc radius
  from the centre at each incremental angle step.
- **Distance tool** — bearing and distance feedback is derived from the
  projected endpoint.

See Also
--------

:doc:`perpendicular` | :doc:`rotate` | :doc:`../development`