這些數學圖形的圖片是如何作的?
12-29
在一個離散微分幾何相關的ppt上看到的圖,作者的所有圖片都是這種風格,感覺很專業,自己也想學著出這樣的圖片。我給作者發了郵件,但很久也沒有得到回復,所以就來麻煩各位了。
我覺得這種圖片風格可能是用某個程序庫編程生成的,或者用數學軟體生成的。因為有些圖形較複雜,還有半透明效果、陰影以及虛線,甚至簡單的lambert shading。M?bius Transformations:
Keenan Crane的slides吧,他自己主頁的FAQ有說, Keenan Crane - Frequently Asked Questions
Question:「How do you create the figures in your course notes?」
Answer:「Right now, the process for creating figures is really a labor of love. I start out in a 3D modeler (Luxology"s modo), where I create the initial geometry, typically as a subdivision surface with a coarse control cage. I render this geometry out in several layers (silhouette, shadows, contour lines, etc.) and then trace over them by hand or using Image Trace in Illustrator. From there I choose the colorization, line styles, etc. For some of the figures I also write custom code (e.g., to construct a certain geometry). Someday I"d love to write a more automated tool, but there are only so many hours in the day! If you think you have a good way of attacking this problem, I"m all ears.」Keenan Crane正好是我暑假project的導師 : ) 他平常花特別多時間在畫這些示意圖上是真的,然後大家戲稱他的配色為Keenan Blue。
P. s. 他自己也提到希望能用到更加自動化的工具。我們組正在開發類似的工具,目前項目還是比較早期的階段。但是如果有人對數學方面的作圖感興趣可以戳:https://penrose.ink。
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