问题
Someone asked me recently if I could print a bracelet with a custom image engraved on its side.
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.
So:
z' = y
y' = r cos(x)
x' = r sin(x)
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.
What I want is either:
an existing module/hack to express this transformation, or
a generic method for performing per-vertex transformations, much like a vertex shader in glsl
At very least, is it possible to confirm such things are not available in OpenSCAD?
回答1:
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()
.
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);}
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
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]);
}
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
Download all scripts
来源:https://stackoverflow.com/questions/26489828/wrap-an-image-around-a-cylinder