将图像环绕在圆柱体周围 [英] Wrap an image around a cylinder
问题描述
最近有人问我是否可以打印一个侧面刻有自定义图像的手镯.
Someone asked me recently if I could print a bracelet with a custom image engraved on its side.
对我来说，问题很简单:我有一个 2d 笛卡尔系统 (x,y)，它表示该人发送给我的矢量化图像的点.我想将这些视为 3d 圆柱系统 (theta, r, z')，其中 r 是常数.最后，我想以通常的方式将这个 3d 圆柱系统转换为 3d 笛卡尔系统 (x',y',z').
To me, the problem is simple: I have a 2d cartesian system (x,y) that expresses the points of the vectorized image the person sent me. I want to treat these as a 3d cylindrical system (theta, r, z') where r is constant. Finally, I want to convert this 3d cylindrical system to a 3d cartesian system (x',y',z') in the usual way.
所以:
z' = y
y' = r cos(x)
x' = r sin(x)
问题是我不知道如何将其表达给 OpenSCAD.有一个使用 multmatrix() 进行矩阵变换的选项，但这仅允许线性变换 - 即我无法表达像 cos(x) 这样的东西，至少据我所知.
The problem is I don't know how to express this to OpenSCAD. There is an option for matrix transformation using multmatrix(), but this only allows for linear transformation - i.e. I can't express things like cos(x), at least to my knowledge.
我想要的是:
一个现有的模块/hack 来表达这种转换，或者
an existing module/hack to express this transformation, or
执行逐顶点变换的通用方法，很像 glsl 中的顶点着色器
a generic method for performing per-vertex transformations, much like a vertex shader in glsl
至少，是否有可能确认这些东西在 OpenSCAD 中不可用?
At very least, is it possible to confirm such things are not available in OpenSCAD?
推荐答案
你可以使用surface()，见http://en.wikibooks.org/wiki/OpenSCAD_User_Manual/The_OpenSCAD_Language#Surface.在外部脚本中计算高度图并将值写入文件，例如'表面.dat'.您可以平移和旋转生成的曲面并在 difference() 中使用它.
you can use surface(), see http://en.wikibooks.org/wiki/OpenSCAD_User_Manual/The_OpenSCAD_Language#Surface. Calculate the heightmap in an external script and write the values in a file, e.g. 'surface.dat'. you can translate and rotate the resulting surface and use it in difference().
我使用此代码和文档中的surface.dat"进行了尝试
I tried it with this code and the 'surface.dat' from documentation
difference() {
translate([0,0,5])cube([10,10,10], center =true);
rotate([0,0,90])surface(file = "surface.dat", center = true, convexity = 5);}
编辑 28.10.2014:以另一种方式，您可以在矩阵中使用像素数据，通过 for 循环和矩阵迭代将像素一个像素地放置在手镯的圆周上.矩阵中的向量包含像素(x)、像素(y)和作为雕刻深度维度的灰度值/255.为了减少形状的数量，可以合并一列的像素，创建一个表示该列深度剖面的多边形并对其进行线性拉伸.在这种情况下，向量包含像素(x)和多边形的点矩阵.我用 Che 的已知图形成功地尝试了它.要生成矩阵，我使用 python3.4、PyQt5 和 Qt.QtGui.QImage.默认情况下，openscad 在 2000 个元素时关闭渲染.您可以在 Edit/Preferences/Advanced 下将其设置为所需的数字
edit 28.10.2014: in another way you can use pixeldata in a matrix to place pixel by pixel on the circumference of the bracelet by a for loop and iteration over the matrix. The vectors in the matrix contain pixel(x), pixel(y) and the greyvalue/255 as dimension for depth of engraving. To reduce the number of shapes the pixels of one column can be pooled, creating a polygon representing the depth-profile of this column and linear-extrude it. In this case the vectors contain the pixel(x) and the pointmatrix of the polygon. I tried it successfully with the known graphic of Che. To generate the matrix i use python3.4, PyQt5 and Qt.QtGui.QImage. By default openscad turns off rendering at 2000 elements. You can set it to the needed number under Edit/Preferences/Advanced
openscad 脚本:
the openscad-script:
include <./matrix_p.scad>;
difference() {
translate([-b,0,0]) rotate([0,90,0]) difference() {
cylinder(h = hb, r = rb, center = false);
translate([0,0,-0.5]) cylinder(h = hb+1, r = rb-tb, center = false);
}
for (val = m)
rotate([-ap*val[0],0,0]) translate([0,-rb-0.1,-ps/2]) linear_extrude(height = ps) polygon(points = val[1]);
}
matrix_p.scad 中的参数设置:
parameter set in matrix_p.scad:
// userinput
rb = 50; //radius bracelet
tb = 5; //thickness of b.
hb = 80; //height of b.
b = 10; //borderwidth beside engraving
// input from Qt.QtGui.QImage
iw = 590; //imagewidth in pixel
ih = 726; //height in pixel
ps = (hb-2*b)/ih; //scaling of pixel to fill the free place
ap = (ps*180)/(PI*rb); //angle per pixel
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