Axonometry
Introduction
Orthogonal axonometry provides a relatively simple method for drawing an orthogonal parallel projection of an object from two associated dihedral views (usually its plan and elevation). It uses the incidence method"), in which the image of the coordinate axes can be chosen (almost) freely, and the relative orientations of the plan and elevation are then determined with the procedure detailed below. The advantages of orthogonal axonometry are:
Method description
Given a three-dimensional coordinate system xyz, the method is based on arbitrarily choosing the projection of the three coordinate axes on the drawing plane (directions), and from these three axes, determining the relative orientation of the plan view (projection on the xy plane) and the elevation view (projection on the yz plane) of an object, which will facilitate its orthogonal axonometric representation using the ray incidence procedure. The resulting projection direction is the normal to the plane represented by the reference triangle, intersection of the aforementioned plane perpendicular to the projection direction, with the three coordinate planes:
Justification of the procedure
An orthogonal parallel projection is uniquely determined by specifying the projection direction. The drawing plane is perpendicular to the projection direction and can be slid along the projection direction as desired without altering the drawing result. To obtain a vivid image of the spatial object, a projection direction must be chosen that is not parallel to any of the three coordinate axes. Therefore, the three coordinate axes intersect the drawing plane at the reference points. By choosing one reference point, the other two are automatically set. The images of the coordinate axes are the heights of the triangle formed by these three points, and the image of the coordinate origin is the intersection of these heights. When the floor plane (xy plane) is tilted around the straight line, the zero point image shifts along the axis to point . The reference points remain unchanged during the turning process. So the line through is the x axis brought down from the drawing plane. Similarly, the folded y axis is obtained, and therefore the undistorted floor plane (xy plane). In order not to alter the axonometric image, the floor plan must be drawn orienting it in the direction of the downward axis. The procedure is analogous for the elevation (yz plane). The two main directions of the resulting incision process are the axis and axis directions.