CN103761376A - Two-dimensional DXF (drawing exchange file) format based three-dimensional realistic display method of parts - Google Patents

Abstract

The invention belongs to the technical field of image processing, and in particular relates to a three-dimensional realistic display method for parts based on a two-dimensional DXF file format. The specific steps are as follows: Step 1: Read the data of the busbar and axis in the DXF file format; Step 2: Use the data read in Step 1 to construct a rotating surface; Step 2.1: Use the arc cutting algorithm to calculate the center coordinates of the arc: Step 2.2: Use the rotation forming algorithm to calculate the coordinates of the rotating surface: Step 2.2.1: Cut the known curve horizontally; Step 2.2.2: Cut the points obtained by the horizontal cutting vertically: Step 3: Use the normal vector algorithm Perform lighting effect processing; step 4: use OpenGL function to display the three-dimensional entity. Finally, the three-dimensional realistic display of parts is realized.

Description

3D Realistic Display Method of Parts Based on 2D DXF File Format

technical field

The invention belongs to the technical field of image processing, and in particular relates to a three-dimensional realistic display method for parts based on a two-dimensional DXF file format.

Background technique

In the design and manufacture of actual engineering parts, the rotating body type parts processed by turning and boring occupy a large proportion. In the computer-aided turning system, the main work is carried out around this type of parts. This type of graphics is often two-dimensional graphics drawn by AutoCAD, and it is not convenient for us to observe its three-dimensional structure. The default file format of AutoCAD is DWG format, which is not open to the outside world by AutoCAD, and we cannot process it.

Computer graphics is an emerging subject that has developed rapidly and is widely used in recent years. It mainly studies the principles, algorithms and systems of graphics input, representation, transformation, realistic rendering technology, computing and input graphics. The latest research results of computer graphics have also been widely used in the field of mechanical CAD/CAM. After engineering and technical personnel complete the design of mechanical parts, they often hope to see the three-dimensional renderings of the parts immediately, so as to have an intuitive and perceptual understanding of its structure, so as to evaluate whether the structure and design of the product are reasonable. This requires the use of knowledge of computer graphics for realistic graphics display. However, in the currently widely used CAD/CAM system software, the realistic graphics display function is only used as one of the functional modules by some large-scale software, and the practical realistic display software that can run independently is relatively rare.

The emergence of realistic graphic display technology can be traced back to the mid-1960s. With the development of computer technology and graphics and the emergence of raster displays, coupled with the substantial improvement in the performance of various computer hardware including display memory, the need for massive Generation of realistic graphics with high-speed memory becomes possible. At present, realistic graphics display technology has been widely used in CAD/CAM, virtual manufacturing, simulation training, numerical control simulation and other fields.

In the design and manufacture of actual engineering parts, the rotating body type parts processed by turning and boring occupy a large proportion. In the computer-aided turning system, the main work is carried out around this type of parts. This type of graphics is often two-dimensional graphics drawn by AutoCAD, and it is not convenient for us to observe its three-dimensional structure. The default file format of AutoCAD is DWG format, which is not open to the outside world by AutoCAD, and we cannot process it.

Contents of the invention

Aiming at the deficiencies in the prior art, the present invention provides a three-dimensional realistic display method for parts based on the two-dimensional DXF file format.

The present invention adopts the following steps to carry out: based on the three-dimensional realistic display method of parts in the two-dimensional DXF file format, specifically

Proceed as follows:

Step 1: Read the data of the busbar and axis in the DXF file format; the graphic structure of the rotary part is actually the

Know the axis and generatrix, construct the corresponding surface of revolution.

Step 2: Use the data read in step 1 to construct a surface of revolution;

Step 2.1: Use the arc cutting algorithm to calculate the center coordinates of the arc:

Step 2.2: Calculate the coordinates of the surface of revolution using the rotational forming algorithm:

Step 2.2.1: Transversally cut the known curve:

Step 2.2.2: Carry out vertical cutting on the points obtained by horizontal cutting:

Step 3: Use the normal vector algorithm to perform lighting effect processing;

Step 4: Use the OpenGL function to display the three-dimensional entity.

In the above step 1, the polyline provided by AutoCAD is used to describe the busbar, and at the same time, the axis is identified by setting the line type. In the entity section, the information of the axis and the busbar are respectively stored in LINE and LWPOLYLINE. When reading the data During the process, you can search for the axis whose line type is the center line according to the values of group code 0 and group code 6, and then read the coordinates of the starting point of the axis in sequence according to the file format; The polyline of the bus, and then read the coordinate values of all vertices of the polyline sequentially according to the file format. After the above analysis and processing, the data required for rotational forming can be read into the program for the next step of data manipulation.

The specific process of calculating the center coordinates (xo, yo) of the arc in the described step 2.1 is as follows:

make $l=\sqrt{\frac{{(c-a)}^2+{(d-b)}^2}{2}}$

所以h＝l*bowFrom the definition of camber we know

So h=l*bow

From the triangle relationship in the figure, it can be obtained: r ² -l ² = (rh) ²

the radius of the arc $r=\frac{h^2+l^2}{2\×h}$

make $\mathrm{\ω}=\arctan \left(\frac{d-b}{c-a}\right)$

Then the coordinates of the center of the arc are:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; xo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\\ \mathrm{<span\; class="notranslate">\; the\; yo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\end{array}\right.$

In the formula: let (a, b) be the coordinates of the starting point, (c, d) the coordinates of the end point, l is the length of the chord formed by (a, b) and (c, d), bow is the camber, h is the chord height , ω is the central angle corresponding to l. The specific cutting process of the step 2.2.1 is as follows: uniformly extract several points on the bus line segment by segment, and store their coordinates into three two-dimensional arrays x[1, j], y[1, j], z[1,j]. The number of points taken is controlled by the transverse cutting density in the program. The higher the transverse cutting density is, the closer the generated three-dimensional graphic generatrix is to the original generatrix.

The specific cutting process of the step 2.2.2 is as follows: After the horizontal cutting is completed, the obtained points are three-dimensionally rotated, and the rotation trajectory of each point is calculated for interpolation point coordinates, and the number of interpolation points is controlled by the vertical cutting density. The higher the longitudinal cutting density, the smoother the cross-section of the generated three-dimensional graphics, but it will also lead to an increase in the amount of data. The coordinate point array x[1, j], y[1, j], z[1, j] on the curve can be obtained by the horizontal cutting operation, and the vertical cutting is set to rotate 360° around the x-axis, in order to find the curve The coordinates of n points formed by each point on the rotation trajectory, the rotation step size can be set to t=2π/n, and the rotation transformation matrix is:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="sin\; t"\; filenames="HDA0000455268870000031.png"\; state="\{\{state\}\}">sin</figure-callout></span><figure-callout\; id="0"\; label="sin\; t"\; filenames="HDA0000455268870000031.png"\; state="\{\{state\}\}">\; </figure-callout>}\mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right]$

Let the point on the curve be (x, y, z), then the coordinates after rotation are:

[x ^* y ^* z ^* ]＝[x y z]*T

Right now $\left\{\begin{array}{c}{x}^{*}=x\\ {\mathrm{the\; y}}^{*}=\mathrm{the\; y}\cos t+z\sin t\\ z^{*}=-\mathrm{the\; y}\sin t+z\cos t\end{array}\right.$

The specific steps of described step 3 are as follows: calculate the normal vector, the required condition is the coordinate values of three non-collinear points, and their order of arrangement determines the direction of the normal vector, in the right-hand space coordinate system, set The coordinates of points A, B, and C are known as (x _A , y _A , z _A ), (x _B , y _B , z _B ), (x _C , y _C , z _C ), and calculate the three points The normal vector of the formed plane, the algorithm is as follows:

和

利用空间解析几何的方法，平面法矢量的空间描述为 $\left|\begin{array}{ccc}i& j& k\\ x_{\mathrm{AC}}& y_{\mathrm{AC}}& z_{\mathrm{AC}}\\ x_{\mathrm{BC}}& y_{\mathrm{BC}}& z_{\mathrm{BC}}\end{array}\right|$ First find the vector

and

Using the method of spatial analytic geometry, the space description of the plane normal vector is $\left|\begin{array}{ccc}i& j& k\\ x_{\mathrm{AC}}& {\mathrm{the\; y}}_{\mathrm{AC}}& z_{\mathrm{AC}}\\ x_{\mathrm{BC}}& {\mathrm{the\; y}}_{\mathrm{BC}}& z_{\mathrm{BC}}\end{array}\right|$

in $\left\{\begin{array}{c}{x}_{\mathrm{AC}}=x_A-x_C,{\mathrm{the\; y}}_{\mathrm{AC}}={\mathrm{the\; y}}_A-{\mathrm{the\; y}}_C,z_{\mathrm{AC}}=z_A-z_C\\ x_{\mathrm{BC}}=x_B-x_C,{\mathrm{the\; y}}_{\mathrm{BC}}={\mathrm{the\; y}}_B-{\mathrm{the\; y}}_C,z_{\mathrm{BC}}=z_B-z_C\end{array}\right.$

Expanding the matrix form described by the plane normal vector space, the mathematical expression can be obtained: (y _AC z _BC -z _AC y _BC )i+(z _AC x _BC -z _BC x _AC )j+(x _AC y _BC -x _BC y _AC )k.

Advantages of the present invention are: 1, because multiple typical three-dimensional CAD/CAM software products (AutoCAD, Pro-Engineer, Master CAM, CATIA, UG II, 3DSMAX) all support DXF file format, so the application based on this file format development The program has wide applicability.

2. The surface of revolution is constructed by cutting the known curve horizontally and vertically, and the smoothness of the cross-section of the generated three-dimensional figure is controlled by the cutting density, thus realizing the conversion of two-dimensional figure data to three-dimensional.

3, the present invention utilizes realistic graphic display technology to select OpenGL as a graphic software package to realize a practical interactive realistic graphic display. In this patent, the OpenGL function function has mainly realized the following functions for the graphic file read: Window initialization, graphic drawing function, coordinate transformation function, lighting and material setting, image and texture operation function, wireframe drawing, surface model, volume model processing and other functions. Therefore, through the setting of the object material and the light source, the lighting effect of the real world can be simulated more accurately, and the purpose of realistic display of the three-dimensional entity computer can be achieved. By adding atomization effects and texture maps, some special effects of entities can be displayed.

Description of drawings

Fig. 1 is the general flowchart of the present invention;

Fig. 2 is a schematic diagram of arc cutting;

Fig. 3 is a schematic diagram of longitudinal cutting;

Fig. 4 is a realistic display of graphics of the present invention.

Detailed ways

As shown in Figures 1 to 3, the present invention takes the following steps: based on the two-dimensional DXF file format of the part three-dimensional real

Real sense display method, the specific steps are as follows:

Step 1: Read the data of the busbar and the axis in the DXF file format; the graphic construction of the part of the revolving body is actually to know the axis and the busbar, and construct the corresponding rotating surface.

Step 2: Use the data read in step 1 to construct a surface of revolution;

Step 2.1: Use the arc cutting algorithm to calculate the center coordinates of the arc:

Step 2.2: Calculate the coordinates of the surface of revolution using the rotational forming algorithm:

Step 2.2.1: Transversally cut the known curve:

Step 2.2.2: Carry out vertical cutting on the points obtained by horizontal cutting:

Step 3: Use the normal vector algorithm to perform lighting effect processing;

Step 4: Use the OpenGL function to display the three-dimensional entity.

In the above step 1, the polyline provided by AutoCAD is used to describe the busbar, and at the same time, the axis is identified by setting the line type. In the entity section, the information of the axis and the busbar are respectively stored in LINE and LWPOLYLINE. When reading the data During the process, you can search for the axis whose line type is the center line according to the values of group code 0 and group code 6, and then read the coordinates of the starting point of the axis in sequence according to the file format; The polyline of the bus, and then read the coordinate values of all vertices of the polyline sequentially according to the file format. After the above analysis and processing, the data required for rotational forming can be read into the program for the next step of data manipulation.

The specific process of calculating the center coordinates (xo, yo) of the arc in the described step 2.1 is as follows:

make $l=\sqrt{\frac{{(c-a)}^2+{(d-b)}^2}{2}}$

所以h＝l*bowFrom the definition of camber we know

So h=l*bow

From the triangle relationship in the figure, it can be obtained: r ² -l ² = (rh) ²

the radius of the arc $r=\frac{h^2+l^2}{2\&times;h}$

make $\mathrm{\&omega;}=\arctan \left(\frac{d-b}{c-a}\right)$

Then the coordinates of the center of the arc are:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; xo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\\ \mathrm{<span\; class="notranslate">\; the\; yo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\end{array}\right.$

In the formula: let (a, b) be the coordinates of the starting point, (c, d) the coordinates of the end point, l is the length of the chord formed by (a, b) and (c, d), bow is the camber, h is the chord height , ω is the central angle corresponding to l. The specific cutting process of the step 2.2.1 is as follows: uniformly extract several points segment by segment on the bus, and store their coordinates into three two-dimensional arrays x[1, j], y[1, j], z[1,j]. The number of points taken is controlled by the transverse cutting density in the program. The higher the transverse cutting density is, the closer the generated three-dimensional graphic generatrix is to the original generatrix.

The specific cutting process of the step 2.2.2 is as follows: After the horizontal cutting is completed, three-dimensional rotation is performed on the obtained points, and the interpolation point coordinates are calculated for the rotation trajectory of each point, and the number of interpolation points is controlled by the vertical cutting density. The higher the longitudinal cutting density, the smoother the cross-section of the generated three-dimensional graphics, but it will also lead to an increase in the amount of data. The coordinate point array x[1, j], y[1, j], z[1, j] on the curve can be obtained by the horizontal cutting operation, and the vertical cutting is set to rotate 360° around the x-axis, in order to find the curve The coordinates of n points formed by each point on the rotation trajectory, the rotation step size can be set to t=2π/n, and the rotation transformation matrix is:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="sin\; t"\; filenames="HDA0000455268870000031.png"\; state="\{\{state\}\}">sin</figure-callout></span><figure-callout\; id="0"\; label="sin\; t"\; filenames="HDA0000455268870000031.png"\; state="\{\{state\}\}">\; </figure-callout>}\mathrm{<span\; class="notranslate">\; </span>}\mathrm{<span\; class="notranslate">t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right]$

Let the point on the curve be (x, y, z), then the coordinates after rotation are:

[x ^* y ^* z ^* ]＝[x y z]*T

Right now $\left\{\begin{array}{c}{x}^{*}=x\\ {\mathrm{the\; y}}^{*}=\mathrm{the\; y}\cos t+z\sin t\\ z^{*}=-\mathrm{the\; y}\sin t+z\cos t\end{array}\right.$

The specific steps of described step 3 are as follows: calculate the normal vector, the required condition is the coordinate values of three non-collinear points, and their order of arrangement determines the direction of the normal vector, in the right-hand space coordinate system, set The coordinates of points A, B, and C are known as (x _A , y _A , z _A ), (x _B , y _B , z _B ), (x _C , y _C , z _C ), and calculate the three points The normal vector of the formed plane, the algorithm is as follows:

和

利用空间解析几何的方法，平面法矢量的空间描述为 $\left|\begin{array}{ccc}i& j& k\\ x_{\mathrm{AC}}& y_{\mathrm{AC}}& z_{\mathrm{AC}}\\ x_{\mathrm{BC}}& y_{\mathrm{BC}}& z_{\mathrm{BC}}\end{array}\right|$ First find the vector

and

Using the method of spatial analytic geometry, the space description of the plane normal vector is $\left|\begin{array}{ccc}i& j& k\\ x_{\mathrm{AC}}& {\mathrm{the\; y}}_{\mathrm{AC}}& z_{\mathrm{AC}}\\ x_{\mathrm{BC}}& {\mathrm{the\; y}}_{\mathrm{BC}}& z_{\mathrm{BC}}\end{array}\right|$

in $\left\{\begin{array}{c}{x}_{\mathrm{AC}}=x_A-x_C,{\mathrm{the\; y}}_{\mathrm{AC}}={\mathrm{the\; y}}_A-{\mathrm{the\; y}}_C,z_{\mathrm{AC}}=z_A-z_C\\ x_{\mathrm{BC}}=x_B-x_C,{\mathrm{the\; y}}_{\mathrm{BC}}={\mathrm{the\; y}}_B-{\mathrm{the\; y}}_C,z_{\mathrm{BC}}=z_B-z_C\end{array}\right.$

Expanding the matrix form described by the plane normal vector space, the mathematical expression can be obtained: (y _AC z _BC -z _AC y _BC )i+(z _AC x _BC -z _BC x _AC )j+(x _AC y _BC -x _BC y _AC )k.

As shown in Figure 4, the present invention utilizes the OpenGL function function to mainly realize the following several functions to the graphics file read: window initialization, graphics drawing function, coordinate transformation function, illumination and material setting, image and texture operation function, line Block diagram, surface model, volume model processing and other functions. Therefore, through the setting of the object material and the light source, the lighting effect of the real world can be simulated more accurately, and the purpose of realistic display of the three-dimensional entity computer can be achieved. By adding atomization effects and texture maps, some special effects of entities can be displayed.

Claims (5)

1. The three-dimensional realistic display method of parts based on the two-dimensional DXF file format is characterized in that: the specific steps are as follows: Step 1: Read the busbar and axis data in the DXF file format; Step 2: Use the data read in step 1 to construct a surface of revolution; Step 2.1: Use the arc cutting algorithm to calculate the center coordinates of the arc: Step 2.2: Calculate the coordinates of the surface of revolution using the rotational forming algorithm: Step 2.2.1: Transversally cut the known curve: Step 2.2.2: Carry out vertical cutting on the points obtained by horizontal cutting: Step 3: Use the normal vector algorithm to perform lighting effect processing; Step 4: Use the OpenGL function to display the three-dimensional entity. 2. The three-dimensional realistic display method for parts based on the two-dimensional DXF file format according to claim 1, characterized in that: in the described step 1, the polyline provided by AutoCAD is used to describe the busbar, and simultaneously by setting the line In the entity section, LINE and LWPOLYLINE respectively store axis and busbar information. In the process of reading data, you can search for the axis whose line type is the center line according to the values of group code 0 and group code 6. , and then read the coordinates of the starting point of the axis in sequence according to the file format; for polylines, first search for the polyline as a bus according to the subclass tag value, and then read all the vertex coordinates of the polyline in sequence according to the file format. 3. the three-dimensional realistic display method of parts based on the two-dimensional DXF file format according to claim 1, is characterized in that: the specific process of calculating the center of circle coordinates (xo, yo) of the arc in the described step 2.1 is as follows: make $l=\sqrt{\frac{{(c-a)}^2+{(d-b)}^2}{2}}$ From the definition of camber we know

So h=l*bow From the triangle relationship in the figure, it can be obtained: r ² -l ² = (rh) ² the radius of the arc $r=\frac{h^2+l^2}{2\&times;h}$ make $\mathrm{\&omega;}=\arctan \left(\frac{d-b}{c-a}\right)$ Then the coordinates of the center of the arc are: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; xo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\\ \mathrm{<span\; class="notranslate">\; the\; yo</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\end{array}\right.$ In the formula: let (a, b) be the coordinates of the starting point, (c, d) the coordinates of the end point, l is the length of the chord formed by (a, b) and (c, d), bow is the camber, h is the chord height , ω is the central angle corresponding to l. 4. The three-dimensional realistic display method for parts based on two-dimensional DXF file format according to claim 1, characterized in that: the specific cutting process of the described step 2.2.1 is as follows: uniformly extract several points segment by segment on the bus , and store their coordinates into three two-dimensional arrays x[1, j], y[1, j], z[1, j]. 5. The three-dimensional realistic display method for parts based on the two-dimensional DXF file format according to claim 1, characterized in that: the specific cutting process of the step 2.2.2 is as follows: after the horizontal cutting is completed, the obtained points are Three-dimensional rotation, and interpolation point coordinate calculation for the rotation trajectory of each point: the coordinate point array x[1, j], y[1, j], z[1, j] on the curve can be obtained by the horizontal cutting operation, Assuming that the longitudinal cutting is a 360° rotation around the x-axis, in order to obtain the coordinates of n points formed by each point on the curve on the rotation trajectory, the rotation step size can be set to t=2π/n, and the rotation transformation matrix is : $\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right]$ Let the point on the curve be (x, y, z), then the coordinates after rotation are: [x ^* y ^* z ^* ]＝[x y z]*T Right now $\left\{\begin{array}{c}{x}^{*}=x\\ {\mathrm{the\; y}}^{*}=\mathrm{the\; y}\cos t+z\sin t\\ z^{*}=-\mathrm{the\; y}\sin t+z\cos t\end{array}\right.$ 5. The three-dimensional realistic display method for parts based on two-dimensional DXF file format according to claim 1, characterized in that: the specific steps of step 3 are as follows: to calculate the normal vector, the required conditions are three different The coordinate values of the points on the line, their arrangement order determines the direction of the normal vector, in the right-hand space coordinate system, the coordinate values of the known points A, B, C, are respectively (x _A , y _A , z _A ), (x _B , y _B , z _B ), (x _C , y _C , z _C ), calculate the normal vector of the plane composed of three points, the algorithm is as follows: First find the vector and

Using the method of spatial analytic geometry, the space description of the plane normal vector is $\left|\begin{array}{ccc}i& j& k\\ x_{\mathrm{AC}}& {\mathrm{the\; y}}_{\mathrm{AC}}& z_{\mathrm{AC}}\\ x_{\mathrm{BC}}& {\mathrm{the\; y}}_{\mathrm{BC}}& z_{\mathrm{BC}}\end{array}\right|$ in $\left\{\begin{array}{c}{x}_{\mathrm{AC}}=x_A-x_C,{\mathrm{the\; y}}_{\mathrm{AC}}={\mathrm{the\; y}}_A-{\mathrm{the\; y}}_C,z_{\mathrm{AC}}=z_A-z_C\\ x_{\mathrm{BC}}=x_B-x_C,{\mathrm{the\; y}}_{\mathrm{BC}}={\mathrm{the\; y}}_B-{\mathrm{the\; y}}_C,z_{\mathrm{BC}}=z_B-z_C\end{array}\right.$ Expanding the matrix form described by the plane normal vector space, the mathematical expression can be obtained: (y _AC z _BC -z _AC y _BC )i+(z _AC x _BC -z _BC x _AC )j+(x _AC y _BC -x _BC y _AC )k.

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