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(4) Cross correspond the output data of the range operator through the crossreference operator.
The shape of minimal surface can be simulated by isosurface algorithm, and its V value can be directly provided by minimal surface equation.
For centuries, human beings have been trying to describe the world in scientific ways, but mathematics makes this work easier.
(10) Give the box of the boundary range to the box input of the isosurface operator; Give the isosurface formula to its V input; Assign the grid accuracy value to its three inputs: Xres, yres and zres; The value of isovalue input is -0.196178; Give a true Boolean value to its merge input to make the generated mesh smoother.
For example, digital patterns in sunflowers, seed multiplication factors, and even mathematical formulas can be used to predict the emergence of black holes.
The creativity of the scheme comes from the three-dimensional geometric model “Mobius ring” of Western Mathematical classics.
The development of modern mathematics has greatly enriched the theory of geometry, enhanced its ability to solve practical problems, and provided diversified tools with the help of computer to design, analyze and build complex forms efficiently.
(7) Assign the decomposed x, y and Z coordinates to the X, y and Z inputs of the evaluate operator respectively, and click + to increase the Z input by enlarging the operator.
It should be noted that the box created here is not the boundary range of the minimal surface, but a parameter used to control its density.
The following will introduce several commonly used minimal surfaces: (1) the formula of gyroid surface gyroid surface is cos (x) * sin (y) + cos (y) * sin (z) + sin (x) * cos (z).
The following are the specific methods of the case: (1) create a box with density control with centerbox operator, and its X, y and Z inputs are assigned 9, 8 and 6 respectively.
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(9) Use the centerbox operator to create a boundary range box, and assign the values of 6, 5 and 4 to its X, y and Z inputs respectively.
Replace the surface formula in the gyroidsurface case with the neovussurface formula, and adjust the X, y and Z parameters of density control to 7, 6 and 5 to obtain the results as shown in the figure.
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It should be noted that the box established here is the boundary range of the minimal surface.
Although its positive and negative connection, up and down connection and internal and external connection form comes from the west, it is similar to the Oriental architectural spirit of the unity of heaven and man and natural Taoism.
（2） Neovussourface because the method of constructing minimal surface is consistent, you only need to replace the formula in the program, and adjust the parameters of density control and isovalue.
(18) Change the values of X, y and Z variables named “density control” and adjust the isovalue parameter to obtain the minimal surface under different densities.
(14) The sphere is scaled in three axes by scalenu operator, and the scaling scales in X, y and Z directions can be set as 4.5, 4 and 3 respectively.
The formula of neovussourface is: 3 * (COS (x) + cos (y) + cos (z)) + 4 * cos (x) * cos (y) * cos (z).
Use listitem operator to extract the mesh with index value of 1 to obtain the minimal surface of irregular body.
(18) To create a mesh shape with thickness, you can bake the result to rhino space and thicken it with the offset mesh command.
It is ubiquitous from the initial form selection to the final construction.
(12) The geometric center point of the boundary box is extracted by the volume operator.
Pythagoras, a Greek mathematician, said: everything is counted.
Replace the surface formula in the gyroidsurface case with the schwarzpsurface formula, and adjust the X, y and Z variables of density control to 9, 7 and 6 to obtain the results as shown in the figure..
In the mathematical concept, minimal surface refers to the surface with zero average curvature.
(3) Subtract 1 from the value named “mesh precision” through the subtraction operator, and give the result to the N input of the range operator.
(2) Use the numberslider operator to create a value with a size of 30 and assign it to the number operator.
Natural phenomena such as flowers, trees, wind, snow, rain and dew in nature hide the mystery of mathematics.
Here, the reader can set the scaling factor by himself, as long as its range does not exceed the boundary of the minimal surface.
Click “+” to increase the number of input terminals by amplifying the operator.
In order to ensure the simplicity of the program interface, the connection between the two operators can be hidden.
(8) Enter “cos (x) * sin (y) + cos (y) * sin (z) + sin (x) * cos (z)” in the panel and assign it to the f input of the evaluate operator.
Since the discovery of minimal surface formula belongs to the field of mathematics, the design industry can directly use the existing formula.
With the development of computer graphics, minimal surface is more and more used in different design fields because of its rich shape change and fluidity.
Finally, the ellipsoid is used to cut the mesh to generate a minimal surface with smooth effect.
Name the two operators “mesh precision” at the same time.
(13) Create a sphere based on the geometric center point through the sphere operator.
(16) The minimal surface mesh is cut with the sphere mesh through the meshsplit operator.
The values assigned to the X, y and Z inputs can be named “density control”.
(17) After the minimal surface mesh is divided, two parts will be generated.
（3） The formula of schwarzpsurfaceschwarzpsurface is cos (x) + cos (y) + cos (z).
The main logical construction idea of this case is to first create a certain number of three-dimensional bisectors within a box, determine the range of isosurface by the minimal surface formula, and then fit the isosurface in the form of grid by isosurface algorithm.
(6) The three-dimensional bisection points are decomposed into x, y and Z coordinates by deconstruct operator.
(5) The data of the three outputs of the crossreference operator are given to the U, V and W inputs of the evaluatebox operator respectively.
(15) Convert the scaled sphere to mesh through the meshbrep operator.
The application of minimal surface in architecture can produce continuous flow surface, such as Taichung national opera house.
(11) The generated mesh shape is smoothed with the smoothmesh operator.