The purpose of reverse engineering redesign of free-form surface is to redesign the real free-form surface by modification and optimization, form the final usable result data, output the parts list, bill of materials or NC machining code instructions, and finally get the new molded products that can be put on the market. Its connotation transcends the development stage of physical model imitation and is intended to be innovative. Many scholars have studied the redesign of reverse engineering to promote the process of reverse engineering in industrial application. Based on practical engineering application, in order to facilitate the further modification and optimization of physical computer model, the author puts forward a regional redesign method for reverse engineering redesign of free-form surfaces.
1 regional redesign method
Put forward the question of 1. 1
NURBS surface reconstruction is often used in reverse engineering of free-form surfaces. Theoretically, the redesign method based on NURBS surface reconstruction can be summarized as modifying and optimizing the surface by changing any one or more control vertices, weight factors and node vectors. In fact, in order to facilitate interactive operation and intuitive consideration, it is mainly manifested in the change of control points.
Aiming at the characteristics of dense distribution of control vertices, large range of surface to be modified and large range of surface adjustment in NURBS surface reconstruction method, an interactive redesign method of NURBS surface by modifying control vertices by region is proposed, which avoids the bad phenomena such as cusp caused by modifying only a single control vertex. If multiple control vertices are modified separately, it will increase the complexity of interactive operation and make the surface shape difficult to control.
1.2 Regional Redesign Thought
The basic idea of regional redesign is that when the control vertices are densely distributed and the changing trend of local surface modification can be accurately or approximately expressed by analytical formula, one control vertex in the design surface domain to be modified is selected interactively, and other control vertices that control the shape change of the region will also change regularly, thus changing the shape of the regional surface. Among them, the interactively selected control vertex is called the main modification control point or the central control point; Those control vertices that decide the corresponding changes are called follow-up control points, and the control grid area where they are located is called the range (or influence domain) of the main control vertices.
The selection of the main modification control point can be determined according to the change center of the surface to be modified, that is, the main modification control point is approximately the center of the range. The range of the range is determined according to the range or constraint conditions of surface modification, and its shape can be a user-defined geometric shape or a random shape determined according to the judgment that the constraint conditions are met.
In the process of method derivation, the range selection is based on a single-valued surface, that is, the curve is projected to the -l coordinate plane, and each pair of (,y) coordinates corresponds to a unique value, as shown in figure 1, figure 1a) is a surface that needs to be redesigned, and the result is rendered. Figure 1b) is its projection, and the point on the projection plane is the projection of the control point.
The custom range shape in the projection plane can be round, rectangular, oval, etc. as needed, and the center of the range projection is the main modification control vertex projection. However, when the surface is binary, the range selection of projection method can also be applied. The origin of the user coordinate system can be established in the center of the binary surface, and the projection field can be set as vector projection according to the value, thus avoiding the confusion of the range. The variation amplitude of the subsequent control points is determined by the variation amplitude and variation law of the master vertex, and the selection of variation law can be determined according to the shape of the original surface and the shape to be obtained. For example, the relationship between the change amplitude of the master modification control vertex and the slave control vertex can be linear, parabolic and hyperbolic.
For the graph 1, the selected influence domain is a circular domain centered on the main control point (as shown in Figure 2a), and the change law between control points is linear. The' point' in Figure 28 is the projection of the main control point on the projection plane, and the range contained by the circle is the circle influence domain. B) For the control points that change linearly and the curves generated by their control, the' point is still the main control point, the' ■' point is the control point that changes linearly with the main control point in the affected area, the curve controlled by the' point is the curve generated after the change, the '●' point is the original surface control point, and the controlled curve is the original curve.
Let the radius of circular influence zone in the projection plane be r, the main control point be d, the coordinate change be (,△y,), the changed main control point be di, and the change vector be △,,; The control point in the influence domain is also called follow-up control point D, and the changed follow-up control point is dl: and the change vector is Adm；; The variation relationship is linear AD = k ad+b, b is constant, and k is the variation proportional coefficient. In order to ensure that the changes of points on and outside the boundary of the influence domain are zero, in this example, let b=0 and k = (r-r)/ruler, where r is the projection distance from the servo control point to the main control point. Then the coordinate changes of the subsequent control points Ad: each is
It can be seen from the formula (1) that the position of the follow-up control point and the change of the main control point are closely related to the distance between the follow-up control point and the main control point. Fig. 3 is a schematic diagram of the linear variation law based on the circular influence domain. The coordinate axis △dl is the variation of control points in the influence domain, and the coordinate axis △trys. Is the change of the main control point, and the coordinate axis r is the distance from the control point to the control point.
The result of the redesign is shown in Figure 4, where a) is the redesigned control grid shape and b) is the redesigned surface, and the result is presented.
Simulation and Verification of Two Examples of China Paper Download Center
In the simulation verification of an example, the reconstructed surface of human upper body based on medical plastic surgery technology is selected for redesign as the application background of reverse engineering. According to the needs and structural characteristics of the body surface, the circular domain is selected as the influence domain, and the linear type is the change relationship. The result of redesign is shown in Figure 5-8.
When the human body is redesigned, the range of the circular influence area of the main control point, that is, the projection diameter, can be set by itself according to the human body characteristics. If the setting range is very small, it can be approximated as the case that only 1 control point is modified, and the result is shown in Figure 9- 12 0.
As can be seen from the corresponding picture in Figure 9- 12, only modifying 1 control points cannot satisfy the aesthetic effect of redesign. If only 1 control point is modified at a time, in order to achieve satisfactory results, multiple control points may be adjusted and modified several times, and the degree of control is difficult to predict.
By using the regional redesign method, the appropriate influence domain can be selected for redesign according to the scope and shape characteristics of the surface to be modified, and the redesigned results can be redesigned while maintaining the main characteristics of the original surface, and the interactive redesign is simple and easy.
3 Conclusion
The simulation results show that the regional redesign method is feasible in practical application. Using this redesign method can avoid the bad influence caused by modifying a single control point in reverse engineering redesign, and bring convenience to the redesign of free-form surface reverse engineering. In addition, due to the change law of control points and the introduction of influence domain, the redesigned surface is easy to predict and control In the example verification, although it is a regional redesign simulation based on human body shaping technology, this method can also be applied to other industrial fields. Posted in China Paper Download Center.