"Projection" Projection and View PPT (Lesson 2)

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"Projection" Projection and View PPT (Lesson 2)

Part One: Learning Objectives

Understand the meaning of orthographic projection of objects and be able to draw the orthographic projection of simple figures based on the properties of orthographic projection.

Projection PPT, part 2: exploring new knowledge

The figure shows that a triangle ruler forms a projection when illuminated by light. What is the difference between the projection lines in Figure (1) and Figures (2) and (3)? What is the difference between the positional relationship between the projection line and the projection surface in Figures (2) (3)?

The projection lines in Figure (1) are concentrated at one point to form a central projection;

In Figures (2) and (3), the projection lines are parallel to each other, forming parallel projections;

In Figure (2), the projection line illuminates the projection surface obliquely;

In Figure (3), the projection line illuminates the projection surface vertically (that is, the projection line is facing the projection surface). We also call this situation that the projection line is perpendicular to the projection surface. Like Figure (3), the projection produced by the projection line perpendicular to the projection surface is called orthographic projection.

In actual cartography, people often use orthographic projection.

As shown in the picture, place a straight thin wire (recorded as line segment AB) in three different positions:

(1) The wire is parallel to the projection surface; (2) The wire is inclined to the projection surface;

(3) The wire is perpendicular to the projection surface (the wire does not necessarily have to intersect with the projection surface).

What are the current status of the orthographic projection of the wire in the three situations?

As shown in the figure, place a square piece of cardboard P (denoted as square ABCD) in three different positions:

(1) The cardboard is parallel to the projection surface; (2) The cardboard is inclined to the projection surface;

(3) The cardboard is perpendicular to the projection surface.

What is the current status of the orthographic projection of cardboard in the three situations?

Projection PPT, the third part: analysis of example questions

Example: Draw the orthographic projection of the cube placed as shown in the figure on the projection surface.

(1) One face ABCD of the cube is parallel to the projection surface;

(2) One surface ABCD of the cube is inclined to the projection surface, the bottom surface ADEF is perpendicular to the projection surface, and its diagonal AE is perpendicular to the projection surface.

Analysis: (1) When the cube is in the position shown in the figure, one face ABCD of the cube and the other face opposite to it are parallel to the projection surface. The orthographic projection of these two faces is exactly the same shape and size as one face of the cube. Square A'B'C'D'. The four sides of the square A'B'C'D' are the projections of the remaining four faces of the cube (these faces are perpendicular to the projection plane). Therefore, the orthographic projection of the cube is a square.

(2) When the cube is in the position as shown in the figure, its surface ABCD and surface ABGF are inclined to the projection surface, and their projections are rectangles A'B'C'D' and A'B'G'F' respectively; the rest of the cube The projections of the two sides are also the above-mentioned rectangles; the projections of the upper and lower bottom surfaces are line segments D'F' and C'G' respectively. Therefore, the projection of the cube is the rectangle F'G'C'D', where the line segment A'B' divides the rectangle into two.

Projection PPT, Part 4: Classroom Exercises

1. Draw the orthographic projection of the following figure.

(1) The projection line shoots from the left to the right of the object;

(2) The projection line shoots from the top to the bottom of the object.

2. There is a round tabletop with a diameter of 1 meter and a table leg height of 1.2 meters (not counting the thickness of the tabletop). As shown in the picture, there is a light 2.5 meters directly above the table. Can you measure the area of ​​the shadow of a round tabletop on the ground when the lights are turned on at night? Why? (Take π=3.14, accurate to 0.1 meters)

Projection PPT, Part 5: Class Summary

1. The meaning and properties of orthographic projection.

2. The projection produced by the projection line perpendicular to the projection surface is called orthographic projection.

3. When a certain surface of an object is parallel to the projection surface, the orthographic projection of this surface has exactly the same shape and size as this surface.

Keywords: Free download of PPT courseware for mathematics in the second volume of the ninth grade of the People's Education Press, download of projection PPT, download of projection and view PPT, .PPT format;

For more information about the "Projection and View Projection" PPT courseware, please click on the Projection and View PPT Projection PPT tab.

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Update Time: 2024-11-06

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