What are Isometrics?

Place the shape so that its three coordinate axes have the same angle (35 ° 16 ) with the axonometric projection plane, and then make an orthographic projection onto the axonometric projection plane. An isometric drawing made in this way is called a positive isometric drawing.

Isometric

Place the shape into three pieces

Formation of axonometric projections

With the object, along with its rectangular coordinate system, along a direction that is not parallel to any coordinate plane, use

Formation of isometric projection

The projection direction S of the isometric projection is perpendicular to the axonometric projection room P, as shown in FIG. A, and the three coordinate planes determining the spatial position of the object and the axonometric projection plane are inclined, and the three orthogonal coordinate axes and axes thereon The inclination angles of the projection planes are all equal, and the shape and size of the isometric projection of the plane graphics parallel to the three coordinate planes on the object change the same. Therefore, the stereoscopic projection of the object's isometric projection is quite strong.

Axial angle and axial expansion coefficient of the isometric projection

1.Angle between shafts

In the isometric projection, since the three orthogonal coordinate axes on the object and the inclination of the axonometric projection plane are equal, the angles between the corresponding isometric axes must also be equal, that is, XOY = YOZ = XOZ = 120 °, as shown in Figure a.

2.Axial expansion coefficient

The axial expansion coefficients of the OX, OY, and OZ axes are equal in the isometric projection, that is, p = q = r. After mathematical derivation: p = q = r0.82. For the convenience of drawing, the simplified axial expansion coefficient p = q = r = 1 is taken. In this way, the drawn figures are enlarged to 1 / 0.82 1.22 times along the length of each axial direction, as shown in Figure c.

Plane solid isometric drawing method

When drawing an isometric drawing from a multi-faceted orthographic projection, the appropriate coordinate system should be selected first and drawn.

Corresponding axonometric axis, then, according to a certain method, draw a plane stereo

The basic method is to draw the axonometric drawing of each vertex according to the coordinates, which is called the coordinate method, see the figure on the right

Two cases.

Drawing method of curved isometric isometric drawing

For example, the drawing in the right album.

Example of drawing method of isometric drawing of curved solid (6 photos)