What polygon is the water cube?

Question 1: How does the structure of the water cube approach the water cube? The first thing that attracts people's attention is the air pillows of different shapes that wrap the whole venue. The building envelope of "Water Cube" is an inner and outer two-layer ETFE (ethylene-tetrafluoroethylene * * *) membrane structure, which consists of more than 3,000 air cushions with an area of 1 1 1,000 square meters. These air pillows vary in size and shape, ranging from 90 square meters to less than 1 square meter. So what is the membrane of "Water Cube"? The application of ETFE in "Water Cube" membrane structure is the first time in China. According to Founder, the representative of the design unit and the executive director of the design consortium of China Construction National Swimming Center, this material is light in texture, but its strength is beyond imagination. After the air cushion is inflated, there is no problem when the car runs over it. In addition, the ductility, fire resistance and heat resistance of this material are also outstanding. "For example, ductility will not break when it is pulled to three or four times its own length. When it reaches above 280 degrees Celsius, it can be burned into a hole, but it does not spread, there is no smoke, and no combustible materials fall. " Birds are a potential threat to the membrane structure: their claws hook on the surface of the air pillow, which is easy to scratch the surface. To this end, a very thin layer of steel wire mesh was designed at the top of the "Water Cube" to prevent birds from flying down. In addition, in order to prevent man-made destruction, a "moat" was specially designed around the "Water Cube". Inside the venue, the membrane structure is built from the second floor. Only when the audience finds the' bubble bar' along a spiral staircase from the southeast entrance can they touch the film with their own hands. Many people are also worried that the membrane will be easily punctured by sharp objects. Founder explained that the membrane structure of "Water Cube" is not as fragile as many people suspect. "Even if the glass is installed outside, it will be in danger of being broken. In fact, this kind of membrane is relatively strong and can only be punctured with a very sharp tool. To say the least, even if there is local damage, it will not affect the whole. Each air pillow is independent, and the air pump will automatically inflate. In addition, it is very easy to repair the surface with special ETFE tape, just like we stick things with scotch tape. " ETFE membrane has strong self-cleaning. Founder told reporters that the friction coefficient of this material is very small, so it is not easy to attach dust. Even if some dust is stuck, the film can be washed clean immediately with a little rain or water. Steel structure: space polyhedron; Use GPS positioning technology; Unloading settlement is only 8 1mm "water cube", and the surface is soft and moist. In fact, the total number of steel members supporting the "water cube" is 305 13, and the number of connecting ball nodes is 9843. Everyone in the industry knows that the steel structure design and construction of "Water Cube" is no less difficult than "Bird's Nest". If you build a traditional house, it's just beams and vertical walls, all on the same plane. In order to create the feeling of water molecules, each air cushion of the "Water Cube" is an irregular polyhedron, so the required steel structure is completely a three-dimensional 12 or 14 polyhedron. It is the first time to build such a steel structure in the world. Because the components of the "water cube" are irregular polygons, if the plane is welded and hoisted as a whole, the error of multi-point aerial positioning connection is difficult to control, and the accumulated error snowballs, so the engineering quality cannot be guaranteed. Engineers tried GPS positioning, laser positioning and other methods, which greatly improved the progress of the project by three times. More than 30,000 rods and nearly 1000 connecting balls are quickly and accurately spliced together like piles of wood in the hands of more than 300 top welders who have welded warships, with the help of workers who are specially responsible for seating. Clever construction methods and skilled welding technology have made the progress of the steel structure project of "Water Cube" advance by leaps and bounds, and the welding speed is as high as more than 200 steel bars every day at the peak of the construction site. On the morning of June 16, 2006, with the dismantling of thousands of tons of scaffolding and jacks, the steel structure support system of "Water Cube" was successfully unloaded. After getting rid of the protection of the supporting system, the steel structure system of "Water Cube" fully meets the design requirements. Under the theoretical index of 240mm settlement range, the actual settlement of "water cube" is only 81mm. At this point, the novel and unique "water cube" steel structure has been "erected" by its own strength. Indoor environment: electroplating points adjust natural lighting; There is no condensation in the water temperature of 26 degrees Celsius; 90% of the water is recycled. People who have been to the National Swimming Center can easily find that the "Water Cube" in the sun has many bright spots, which are scattered on the surface of the "Water Cube" like stars. These bright spots are electroplating spots. It is reported that ...

Question 2: Is the polygon on the surface of the water cube flat? Yes, it is.

Question 3: What is the Water Cube? Hello, I'm glad to answer your questions.

Water Cube is an ETFE inflatable pillow structure, that is, just like skin, it is made of space steel frame and uses membrane structure as skin.

Question 4: Super Brain once said that the Beijing Water Cube is an infinitely magnified Tai Sen polygon.

Question: How does 3Dmax make an irregular polygon bulge like a water cube? First, refine the surface, then select the point mode, turn on soft selection, adjust the range, then manually adjust the irregular graphics, and finally turn on smoothing.

If noise is used, the concave-convex effect is basically the same, and there is no sense of reality. The best way is to adjust it manually.

Question 6: Beginners ask how to draw irregular water cubes with CAD. Since all your drawings are marked, you can set up XY coordinates with the center of the circle, and then mark them one by one according to the drawings. This requires you to have a solid CAD foundation, understand mathematics and geometry, and practice slowly!

Question 7: What is an Tai Sen polygon? See Baidu Encyclopedia for details.

Tyson polygon

Tai Sen polygon, also called Voronoi diagram, is named after Georgy Voronoi, and consists of a set of continuous polygons composed of perpendicular lines connecting two adjacent points.

Chinese name Tai Sen polygon

Qualitative polygon

A Tai Sen polygon has the shortest distance from one point to the corresponding discrete point.

American climatologist a? h？ Tyson

brief introduction

Tai Sen polygon is a part of the space plane. Its characteristic is that any position in the polygon is closest to the sampling point (such as residential area) and far from the sampling point in the adjacent polygon, and each polygon only contains one sampling point. Because of the bisection of Tai Sen polygon in space division, it can be used to solve the nearest point problem, the smallest closed circle problem, and many spatial analysis problems, such as adjacency, adjacency and accessibility analysis. [50043.00000000 105

Establishment step

The key to the establishment of Tai Sen Polygon Algorithm is to connect discrete data points into a triangular network reasonably, that is, to construct a Delaunay triangular network. The steps to create a Tai Sen polygon are as follows:

1, discrete points automatically construct triangulation, that is, construct Delaunay triangulation. Number the discrete points and the triangle formed, and record which three discrete points each triangle consists of.

2. Find out the numbers of all triangles adjacent to each discrete point and record them. It only needs to find triangles with the same vertices in the constructed triangulation.

Establishment of Tai Sen Polygon

3. Sort the triangles adjacent to each discrete point clockwise or counterclockwise, so as to connect and generate Tai Sen polygons in the next step. Let the discrete point be O, find a triangle with O as the vertex, and set it as A; Take another vertex of triangle A except O and set it as A, then you can also find another vertex, that is, F; Then the next triangle must be of, which is the triangle f; If the other vertex of triangle F is E, then the side of the next triangle is OE; Repeat this action until you return to the oa side.

4. Calculate the center of the circumscribed circle of each triangle and record it.

5. According to the adjacent triangles of each discrete point, connect the centers of the circumscribed circles of these adjacent triangles to obtain the Tai Sen polygon. For the Tai Sen polygon on the edge of the triangulation, the perpendicular line can intersect with the contour and form a Tai Sen polygon with the contour. [2]

trait

Tai Sen Polygon Legend (2 pieces)

1, each Tai Sen polygon contains only one discrete point data;

2. The distance between the points in the Tai Sen polygon and the corresponding discrete points is the shortest;

3. The distance between the points on the side of Tai Sen polygon and the discrete points on both sides is equal.

Tai Sen polygon region

Because the polygon area of Tai Sen changes with the distribution of point sets, the variation coefficient CV of polygon area (that is, the ratio of standard deviation to average value of polygon area in Tai Sen) can be used to measure the variation degree of convex polygon area, thus evaluating the distribution type of sample points. See formula (1) and formula (2}: see Baidu Encyclopedia for the formula.

Where, Si is the area of the ith polygon, S is the average of polygon areas, N is the number of polygon areas, and R is the variance. When the distribution type of point set is "uniform", the polygon area changes little; when the distribution type of point set is "cluster", the polygon area within cluster is small, while the polygon area between clusters is large, and the CV value is also large. Duyckaert made three suggestions: When the point set is clustered, CV=92% (including >: 64%); When the point set is evenly distributed, CV=29% (including >;

Question 8: What is the structural and static analysis of the Bird's Nest? First of all, although the architectural scheme is foreign, the construction drawings are all structural designs made by domestic first-class architectural design units and national registered structural engineers. There are also engineering geological investigation reports that meet the seismic code. And carried out the highest level of seismic fortification special review of high-rise buildings organized by the Ministry of Construction. 2) The first step of seismic design is to define the seismic fortification requirements, that is, the seismic fortification intensity and ground motion parameters of the building area are stipulated in the seismic parameter zoning map of China and the specific urban seismic fortification intensity in the national code for seismic design of buildings. For example, the seismic fortification intensity of Wenchuan is 7 degrees, and that of Kunming is 8 degrees. The general seismic fortification intensity of 7 degrees is 0. 1g, and that of 8 degrees is 0.2g Because of their special importance, the Bird's Nest and the National Grand Theatre have made special seismic safety assessments, which have improved the ground motion parameters compared with other buildings in Beijing. 3) A higher seismic fortification standard is determined. According to the importance of the building and the number of users, the building is divided into four categories: A, B, C and D. For example, in a third-class A hospital, the fortification intensity and seismic measures should be increased by one degree, and the ground motion parameters used in the design should be determined through special seismic safety evaluation. Teaching buildings in primary and secondary schools are classified as Class B because of their large number of students and weak self-help ability. The seismic action adopted in its design conforms to the local seismic fortification intensity, but the seismic measures should be increased by one degree. Therefore, according to the regulations, all primary and secondary schools in Wenchuan must take 8-degree earthquake-resistant measures and cannot suddenly collapse. General buildings, such as houses, are classified as Class C, and the seismic action adopted in their design is in accordance with the local seismic fortification intensity, without improving seismic measures. Class d is generally warehouses and so on. , the seismic requirements are low. The Bird's Nest and the National Grand Theatre are both Grade A buildings. 4) Start the design. In the design stage, the reasonable structural system of the Bird's Nest and the National Grand Theatre is first determined. Designers will rationally arrange the structural system of the house according to the use function of the house. Low-rise buildings generally adopt cast-in-place concrete frame structure, which has good seismic effect; High-rise buildings or large buildings need frame-shear wall structures to meet the seismic requirements; No matter how high the building is, it should be made into a tube-in-tube structure or directly made into a steel structure. The main structures of the Bird's Nest and the National Grand Theatre are steel structures, which are particularly earthquake-resistant. 5) Seismic mechanical checking calculation and adoption of seismic measures. The anti-seismic function of buildings is reflected in the ability of the structure to resist earthquake vibration and earthquake acceleration. In addition to checking the seismic force, buildings should also take many seismic measures, such as the arrangement of ring beams and structural columns, the reinforcement of supports and other accessories. , also has detailed provisions in the national standard. The Bird's Nest and the National Grand Theatre are strictly implemented. 6) A comprehensive survey of the Bird's Nest and the National Grand Theatre shows that a qualified design generally includes descriptions and drawings of architecture, structure, water supply and drainage, electricity, etc. It also depends on whether other majors meet the seismic design. For example, water supply and drainage pipelines in some earthquake-prone areas should be flexibly connected. The structural design of a building is one thing, but the construction is another. Whether the design can become a real thing depends on choosing the construction unit and strengthening supervision. It is very important for every link in the construction of the Bird's Nest and the National Grand Theatre (1). It is necessary not only to have technical training requirements for workers, but also to have a strict step-by-step acceptance system. Because concrete is a so-called concealed work, the steel bars are tied correctly, and the model and quantity are wrong. As long as the concrete is poured, nothing can be seen. 2) There are many details in the construction, which can never be ignored. Fortunately, for the Bird's Nest and the National Grand Theatre, money is the most important thing, so the best buildings and materials have been used to meet the highest seismic standards.

The steel structure design and construction of "Water Cube" is no less difficult than "Bird's Nest". If you build a traditional house, it's just beams and vertical walls, all on the same plane. In order to create the feeling of water molecules, each air cushion of the "Water Cube" is an irregular polyhedron, so the required steel structure is completely a three-dimensional 12 or 14 polyhedron. It is the first time to build such a steel structure in the world. Because the components of the "water cube" are irregular polygons, if the plane is welded and hoisted as a whole, the error of multi-point aerial positioning connection is difficult to control, and the accumulated error snowballs, so the engineering quality cannot be guaranteed. Engineers tried GPS positioning, laser positioning and other methods, which greatly improved the progress of the project by three times. More than 30,000 chess pieces and nearly 65,438+00,000 connecting balls were delivered by workers who were specially responsible for seating. & gt

Question 9: How to draw irregular polygons in Word Word 2003 provides many kinds of polygons. When the required graphics are not given in the optional graphics list, you can do the following.

(1) Click the "AutoShape → Line → Arbitrary Polygon" option in the drawing toolbar, and the mouse will turn into a cross.

(2) Click the mouse once at the position where the graph needs to be drawn to determine the first vertex of the polygon; Then drag the mouse to pull out the straight line, and click the mouse again to determine the second vertex; Then drag the mouse to pull out the straight line and determine the third vertex in the appropriate position. By analogy, the last vertex and the first vertex can be merged to complete the drawing of the whole polygon.

Question 10: Robinho should not join Real Madrid now. At present, he is not ready. 10 is the same question.

Robinho's position after arriving at Real Madrid

There is still one year before the World Cup.

Is he willing to sit on the bench?

Otherwise Owen may have to leave.

But with Owen's state and admirable professional attitude.

Personally, I don't think we should let go.

Raul will never miss. After all, the local soul Raul is the spiritual pillar of the team.

Put him on the bench and the Spanish fans will not let go of Lucenberg.

Pang Luo is too lazy to be annoying, but he is the first striker in the world after all.

The midfield is even more crowded.

There is no big problem for Qi Zu and Beckham to become the main players.