Principle belt of mathematical photography

When the shadow part of an object is on other objects, how to find the height of the object? As follows:

1. First, we need to measure the length of the object itself and the shadow it casts on other objects.

2. Then according to the principle of similar triangles, the following equation can be obtained: object height/object shadow length = object height/object shadow length.

3. Then, the known shadow length of the object and the shadow length of the object itself are substituted into the above equation to solve the height of the object.

4. Finally, the calculation formula of object height is: object height = object shadow length * object height/object shadow length.

It should be noted that this method is suitable for the case that there is a similar triangles between the object itself and its shadow. If there is no similar triangle between the object and its shadow, then this method can't solve the height of the object.

Extended knowledge: projection

1. Projection principle: Projection principle is a basic principle in optics, which means that the shadow length of an object in a certain direction is proportional to the length of the object itself in that direction. This principle is widely used in photography, film, projection and other fields.

2. similar triangles: similar triangles is a basic concept in mathematics, which refers to two triangles with the same shape but possibly different sizes. The corresponding angles of similar triangles are equal, and the corresponding sides are proportional. When solving practical problems, similar triangles is often used to enlarge or reduce objects for calculation.

3. Shadow length measurement: Shadow length measurement is an optical measurement method. By measuring the shadow length of an object in a certain direction, the length of the object itself in that direction can be calculated. The measurement method of shadow length is simple, but its accuracy is affected by light, environment and other factors.

4. Calculation of object height: The object altimeter is a basic problem in mathematics, which can usually be solved by measuring the length of the object itself and its shadow length, and then applying the projection principle or similar triangles principle. The calculation of object height is widely used in real life, such as architectural survey and photogrammetry.

5. Three-dimensional measurement: Three-dimensional measurement is an optical measurement method. By measuring the length of an object in three directions, the three-dimensional coordinates of the object can be calculated. Three-dimensional measurement methods can measure the shape, size, position and other information of objects, and are widely used in computer graphics, virtual reality, robot vision and other fields.