First, the direct calculation method

For simple geometry, you can directly calculate the area of the shadow part. Such as rectangle, triangle, trapezoid, etc.

Second, the segmentation method

Divide the shadow part and the blank part, calculate the area of each part separately, and then add and subtract to get the area of the shadow part. For example, divide an irregular figure into several regular figures, calculate the area of each regular figure respectively, and then add them to get the area of the shadow part.

Third, the completion method

Complete the shadow part into a complete regular figure, calculate the area of the regular figure, and then subtract the area of the completed part to get the area of the shadow part. For example, complete an irregular figure into a circle or rectangle, calculate the area of the regular figure, and then subtract the area of the completed part to get the area of the shadow part.

Fourthly, the symmetry method.

Using the symmetry of graphics, the shadow part is transformed into regular graphics, and the area of regular graphics is calculated. For example, paint half of a square black and calculate the area of the black part.

Verb (abbreviation of verb) integration method

For the figure surrounded by continuous curve, the area of shadow part can be solved by integral method. For example, solve the area between the function image and the x axis.

Monte Carlo method of intransitive verbs

By random sampling, the area of the shadow part is estimated. For example, throw a large number of points in the figure, count the points that fall in the shadow part, and then divide by the total points to get the area of the shadow part.

Seven, numerical approximation method

By discretizing the grid, the shadow part is approximated as a polygon and the area of the polygon is calculated. For example, a graph surrounded by a curve is discretized into a polygon composed of small meshes, and the area of the polygon is calculated.

The Origin, Contribution and Development of Shadow Area Algorithm

First, the origin of geometry

Shadow area algorithm can be traced back to the origin of ancient geometry. In ancient Greece and Egypt, people began to study the relationship between shape, size and space. They explore the properties and measurement methods of geometric figures by observing the shadows produced by objects in the sun. These early geometricians laid the foundation for the later shadow area algorithm.

Second, the contribution of ancient civilization.

Ancient civilization has made important contributions to the development of shadow area algorithm. For example, the ancient Egyptians used sundials to determine the changes of time and seasons, which required calculating the position of the sun in the sky and the length of shadows. They developed some basic geometric principles and measurement methods, such as similar triangles, proportional relation, etc., and applied them to the later shadow area algorithm.

Third, the development of mathematics.

With the development of mathematics, people's research on shadow area algorithm is gradually deepening. In the Middle Ages, Arab mathematicians introduced the concepts of algebra and trigonometry, which provided new tools for solving the shadow problem of complex shapes. They developed some important geometric theorems and formulas, such as sine theorem and cosine theorem, which played a key role in the shadow area algorithm.