The rotating geometrical figures hold a certain position in relation to a motionless system. Knowing data of the rotating triangle, it is simple to determine the full size of this figure.
It is required to you
- - pencil;
- - notebook.
Instruction
1. It is possible to find the full size of a triangle method of replacement of the planes of a projection. For this purpose a geometrical figure present in the form the level planes when one of protektion is displayed without distortions in relation to the plane.
2. First of all on the set coordinates of points construct a projection of a triangle of ABC. Then carry out the frontal projection of a horizontal of this triangle which is characterized by points of B2 and M2. After that on the binding line find a horizontal projection of a point of M1.
3. That the triangle became projecting, enter additional P4 plane which will be perpendicular to P1 plane. At the same time the axis h1.4 has to be located is perpendicular to B1M1 projection.
4. From each point of the horizontal plane draw the binding lines perpendicular to an axis h1.4. For transformation of a triangle to the plane of level enter one more plane – P5. The axis h4.5 will be located parallel to A4B4C4.
5. From each point of A4B4C4 draw binding lines which will be perpendicular to an axis h4.5. On these lines lay off the distances equal to distance from an axis h1.4 until a horizontal projection of each point.
6. The triangle of ABC reached position which parallel to P5 plane. A5B5C5 projection – the full size of a triangle of ABC.
7. It is possible to determine the full size of a triangle as well by a rotation method. For this purpose at first present a triangle in the form of the projecting plane then turn it around the second set axis, having transformed it to the level plane.