"Projection" Projection and View PPT Courseware 5

Description

"Projection" Projection and View PPT Courseware 5

projection

Generally, when an object is illuminated with light, the shadow obtained on a certain plane (floor, wall, etc.) is called the projection of the object.

The irradiating light is called a projection line

The plane on which the projection is located is called the projection surface.

parallel projection

Sometimes the light ray is a group of parallel rays, such as the rays in a beam of sunlight or searchlight. The projection formed by the parallel rays is a parallel projection.

For example, the shadow formed by an object under sunlight (referred to as the sun shadow) is a parallel projection. The direction of the sun's shadow can reflect the time,

central projection

The projection formed by the light rays emitted from the same point (point light source) is called the central projection.

For example, if an object forms a shadow under the light from a light bulb, it is a central projection.

observe

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 lines illuminate the projection surface obliquely;

(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.

Through observation, we can find:

(1) When the line segment AB is parallel to the projection plane P, its orthographic projection is the line segment A1B1, and the size relationship between the line segment and its projection is AB_____A1B1;

(2) When line segment AB is inclined to the projection plane P, its orthographic projection is line segment A2B2, and the size relationship between the line segment and its projection is AB______A2B2;

(3) When the line segment AB is perpendicular to the projection plane P, its orthographic projection is a ________

As shown in the figure, place a square piece of cardboard P (for example, square ABCD) in three different locations:

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

(2) The cardboard is tilted 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?

induction

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.

Example 1: Draw the orthographic projection of the cube placed as shown on the projection plane P.

(1) One face ABCD of the cube is parallel to the projection plane P

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

Analysis: (1) When the cube is positioned as 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 a square with exactly the same shape and size as one face of the cube. 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 ground 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´ bisects the rectangle.

Example 2 (1) As shown in (1), when the kitten reaches point B, use a line segment to represent its shadow under street lamp A.

(2) As shown in Figure (2), when the kitten reaches point B, according to its shadow under street lamp A, its height is judged and represented by a line segment.

(3) As shown in Figure (3), when the kitten reaches point B, the kitten and its shadow under street lamp A are as shown in the picture. In which direction do you think the position of the street lamp is, and how do you judge it?

Discuss

⑴The picture shows the shadows of two small trees at the same moment. Please draw the light rays that form the shadows of the trees in the picture. Are they the rays of the sun or the rays of lights?

Method: ① Draw a straight line through the top of the big tree and the top of its shadow;

②Draw a straight line through the top of the small tree and the top of its shadow. The two lines intersect at one point.

⑵Is the shadow in the picture formed under sunlight or under light? Draw the shadow of the flagpole at the same time (represented by a line segment).

From the drawing, we can see that the two rays are parallel rays, so they are formed under sunlight.

How to draw: Draw a straight line through the top of the flagpole parallel to a light ray, intersecting the straight line at the bottom of the two trees at one point. The line segment from the bottom of the flagpole to the intersection point is the shadow of the flagpole.

Practice in class

1. Beibei and his father are walking on the beach in the sun. He doesn’t want his father to see his shadow. So can you draw the general range of Beibei’s activities?

As long as Beibei's shadow completely overlaps with his father's shadow, his father can't see his shadow!

2. One afternoon, Teacher Qin first participated in the 200m race and then the 400m race in the school sports meeting. The photographer took photos of her participating in these two races at the same location (as shown below). Which photo do you think is of Teacher Qin participating in the 400m race? Why?

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Update Time: 2024-10-01

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