學習如何使用數學軟體搭配自由軟體，建立數學函數的3D曲面模型以及該模型的列印輸出，使同學能夠透過這個過程，瞭解與熟悉數學函數所代表的代數與幾何關係。
本課程為想要透過Mathematica, OpenSCAD 或 MathMod軟體，使修課同學能夠快速繪出兩個變數以上函數z=f(x,y)的曲面圖形; 進一步討論F(x,y,z)=0的方程式的解所呈現的曲面圖形。由於3D模型必須有一定的厚度，才能透過3D列印機輸出成品，因此當曲面的厚度不足時或有破洞時，利用Meshmixer這個軟體給予上面厚度或修補功能，再進行3D列印。
從本課程，同學會學習將一個函數的圖形繪出，從不同面向觀察3D的呈現方式，最後再進行列印。因此函數不在只是抽象的運算而已，而是垂手可及的真實幾何形體。Learn how to use mathematical software and free software to create a 3D surface model of a mathematical function and print the output of the model. Through this process, students can understand and become familiar with the algebraic and geometric relationships represented by mathematical functions.
This course is for students who want to use Mathematica, OpenSCAD or MathMod software to quickly draw the surface graph of the function z=f(x,y) with more than two variables; further discuss F(x,y,z)=0 The surface graph represented by the solution of the equation. Since the 3D model must have a certain thickness before the finished product can be output through a 3D printer, when the thickness of the curved surface is insufficient or there are holes, the software Meshmixer can be used to provide thickness or repair functions before 3D printing.
From this course, students will learn to draw the graph of a function, observe the 3D presentation from different aspects, and finally print it. Therefore, functions are no longer just abstract operations, but real geometric shapes within easy reach.
教師講義
參考書籍：
1. 賴維祥，3D列印導論，全華書局
2. 3D Printer Tutorial, UP 3D Printer, http://www.pp3dp.com/
3. Henry Segerman, 3D printing for mathematical visualization
4. LOW-COST 3D PRINTING FOR SCIENCE, EDUCATION & SUSTAINABLE DEVELOPMENT
Editors: E. Canessa, C. Fonda, and M. Zennaro, ICTP-The Abdus Salam International Centre for Theoretical Physics, 2013
參考連結：
1. Surfer imaginary, https://www.imaginary.org/program/surfer
2. OpenScad, https://openscad.org/
3. MathMod, Abderrahman Taha, http://sourceforge.net/projects/mathmod/
4. Wolfram Mathematica, http://www.wolfram.com/mathematica
5. Blender Foundation, Blender, http://www.blender.org/
6. Maple, https://en.wikipedia.org/wiki/Maple_(software)
7. K3DSurf, Abderrahman Taha, http://k3dsurf.sourceforge.net/
Teacher Handouts
Reference books:
1. Lai Weixiang, Introduction to 3D Printing, Quanhua Book Company
2. 3D Printer Tutorial, UP 3D Printer, http://www.pp3dp.com/
3. Henry Segerman, 3D printing for mathematical visualization
4. LOW-COST 3D PRINTING FOR SCIENCE, EDUCATION & SUSTAINABLE DEVELOPMENT
Editors: E. Canessa, C. Fonda, and M. Zennaro, ICTP-The Abdus Salam International Center for Theoretical Physics, 2013
Reference link:
1. Surfer imaginary, https://www.imaginary.org/program/surfer
2. OpenScad, https://openscad.org/
3. MathMod, Abderrahman Taha, http://sourceforge.net/projects/mathmod/
4. Wolfram Mathematica, http://www.wolfram.com/mathematica
5. Blender Foundation, Blender, http://www.blender.org/
6. Maple, https://en.wikipedia.org/wiki/Maple_(software)
7. K3DSurf, Abderrahman Taha, http://k3dsurf.sourceforge.net/
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中報告期中報告 interim report |
30 | 說明前半學期的學習心得與自行選定3D模型以及3D列印過程 |
| 期末報告期末報告 Final report |
30 | 說明自行設計的3D模型的數學函數以及3D列印過程 |
| 平時作業和出席平時作業和出席 Daily homework and attendance |
40 |
