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The request is informed from Mr. Svein Daniel Solvenus to Yamamoto in 2011 how we can make 3D display of an egg with the use of the equation described in Yamamoto's website. Therefore, Yamamoto make an equation of egg surface and C program for its calculation. Then, the coordinates data of the egg surface written in an Excel file by calculation are sent to Mr. Daniel. Mr. Daniel create 3D figure of egg using its Excel file, and moreover, create that of apple. 1. Apple Shape
The first model is an egg shape made as like that the egg shaped curve given in Eq.(9b) in the page of Yamamoto's Website is made revolve around x axis. If we introduce the phase angle in (y, z) plane, the egg surface is formulated as |
created by Mr. Svein Daniel Solvenus |
created by Mr. Svein Daniel Solvenus |
However, as seen in Fig.3, this model has the demerit that the holes exist in both sides and the mesh intervals are extremely not uniform.Moreover, it is much difficult that its demerit is removed in this first model. |
Fig.3 The hole existance and non-uniformity of mesh |
Therefore, as the second model, we treat an egg shape which is made rotating the egg curve described in Eq.(1) given in the webpage of "Egg Shaped Curve II" around x axis. If we introduce the phase angle in (y, z) plane, the egg surface is formulated from Eq.(1) in this webpage in the same manner as described in the above as |
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2. Apple shape Though the equation of apple shaped curve in (x, y) plane is given in the Eq.(3) in the page of "apple shaped curve", it is written in the following equation to give 3D display of an apple in accordance to the same process described above. , (3) where 0 < < 2. With the use of the coordinates data calculated by Eq.(3) with computer, Svein Daniel Solvenus creates the 3D displays as seen in Figs.5 and 6. The 3D picture in Fig.6 is very beautiful. Thanks to Mr. Svein Daniel Solvenus. |
created by Mr. Svein Daniel Solvenus |
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