The depth of the shape. Imagine that the plane figures in the geometric sense are all two-dimensional, and they have no depth. But visual experience tells us that once these graphics are regarded as cardboard standing sideways or lying flat on the table, these two-dimensional graphics can represent the imaginary depth space. If we put squares, trapezoids and parallelograms on the table, we will feel that the changing state of trapezoids and parallelograms is like a square lying flat on the table, and they extend to the depth of the table, so some contours have the meaning of depth space, because these figures roughly conform to the law of perspective change. Therefore, it is very important to understand the perspective changes of shapes. Parallel perspective and Angle Perspective draw a horizontal line on the paper. We call this line the horizon, which is used to indicate the height of the eyes when observing objects. When the viewing angle changes, there are one or two groups of vanishing points on the horizon opposite to the rectangle. If one vanishing point is called Parallel perspective and two vanishing points are called angle perspective, these are two common perspective states. The perspective of a horizontally placed rectangle will become a horizontally placed rectangle. The far and near sides are parallel to the apparent horizon, the length of the near side remains unchanged, and the perspective of the far side is shortened. When this rectangle moves vertically in the eye level, the near edges of each figure on the trajectory are equal, and the shortened far edges are actually equal and look unequal, which is caused by illusion. The closer to the horizon, the narrower the surface of the graph, the shorter the left and right borderlines concentrated at the vanishing point, and the smaller the slope, which is the case in Parallel perspective. In angular perspective, the horizontally placed rectangular edge has an angle with the picture and is not parallel to the apparent horizon. When it moves vertically up and down, the vertices of the four corners of each figure on the trajectory are on the corresponding four vertical lines. Their two groups of opposite sides are diagonal to the left and right vanishing points. The closer to the apparent horizon, the narrower the figure and the smaller the slope of the sideline. When the figure is at the height of the apparent horizon, the perspective deformation becomes a straight line. Perspective change of rectangle standing on the edge When the rectangular plane figure with vertical front turns to the vertical edge, its edge will change perspective. The lower set of edges are concentrated in vanishing points, and the left and right sets of edges are parallel to each other and perpendicular to the apparent horizon. Except the length of the near side of the rectangle, the other three sides will be shortened. In two different perspective changes, Parallel perspective and Angle Perspective, the vertical angles of rectangular turning edges are different. When the rectangle is rotated 90 degrees from the front to the side, it is in Parallel perspective, and other states less than 90 degrees, such as 15 degrees, 45 degrees and 80 degrees, are in angular perspective. It can be seen from the beginning: 1: When the rectangle standing sideways moves horizontally, the closer it is to the vertical line of the vanishing point, the narrower it is and the farther it is. 2. The change of the length, direction and angle of the rectangular edge line is closely related to the position of the vanishing point. 3. The simplified surface is closer to the apparent horizon. 4. These perspective changes show the depth of the surface and improve the screen space. 5. In the actual sketch practice, we will meet.

Perspective In order to make a plane successfully present three-dimensional space, Renaissance artists developed various perspective methods, some of which are based on actual observation like traditional classicists, while others are based on geometric mechanics. The actual observer comes from the viewer's visual experience and can express subjective views. For example, andrea mantegna's The Execution of St James (Figure 2) puts the point of view beyond the lower boundary of the picture, resulting in a noble, bold and dramatic composition from bottom to top. However, according to the mechanical measurement of geometry, one or two vanishing points are used to assist the representation of perspective, and the assumed vanishing points in space are used to produce a three-dimensional effect with gradual depth change. Mechanical perspective is based on theoretical concepts, which easily leads to unnatural visual effects; However, if combined with actual observation, artists can express space more orderly and naturally, make the plane appear deep, make the proportion of characters conform to this spatial structure, make the volume and spatial relationship between people and things reconcile with each other, and make the realistic description reach a more perfect realm. For example, the proportion of buildings, floors, stairs and people depicted by Raphael of Yadian College (Figure 3) are carefully constructed according to perspective method to show a deep sense of space. The application of perspective principle in the artistic expression in the Renaissance has become a classical technique that has been highly valued and widely used because it helps to express the three-dimensional realistic space.

A commercial designer needs to make a "demonstration" to express his sudden ideas to customers and artists. Therefore, through perspective and the use of different materials, this course will make the plane image or newly designed product more convincing and stereoscopic, so that the pre-conceived image can be more truly presented and the new concept can be fully expressed to customers and accepted. In this way, designers can achieve the ultimate goal. This course will give examples for learners to practice and master.