You will need
- - the notebook.
Find natural size of the triangle it is possible to method of replacing planes of projection. For this geometric figure present in the form of a level plane when one of the patronage displayed without distortion in relation to the plane.
First, given the coordinates of points, construct the projection of the triangle ABC. Then slide the front horizontal projection of this triangle characterized by points B2 and M2. After that, a connecting line, find the horizontal projection of the point M1.
Below the triangle was projecting an additional plane P4, which is perpendicular to the plane P1. The axis x1,4 should be located perpendicular to the projection of B1M1.
From every point of the horizontal plane guide the connection lines perpendicular to the axis x1,4. To convert the triangle in the plane of the level, enter another dimension – P5. The axis x4,5 is located in parallel A4B4C4.
From each point A4B4C4 guide the connection lines, which are perpendicular to the axis x4,5. On these lines put the distance equal to the distance from the axis x1,4-horizontal projection of each point.
Triangle ABC has taken a position which is parallel to the plane A5. Projection A5B5C5 – the actual size of the triangle ABC.
To determine the natural size of the triangle you can also and method of rotation. To do this, first imagine a triangle in a projective plane, then rotate it around a second given axis, converting it to a plane level.
Be careful when constructing the projection of a triangle: if you make a mistake, the result will be incorrect.
The angle formed by the projection of the triangle А4В4С4 and the coordinate axis, - tilt angle of a given triangle ABC to the plane P1.