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Newbie with rotation problem

Ronaldo

Sat, Apr 2, 2016 8:10 PM

doug.moen wrote

The second from the left is a sphere.
All the rest could be done using cylinder.
The middle could be a cube.
The second from right could be a sphere.

Right.
Right.
Wrong.
Right.

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doug.moen wrote > The second from the left is a sphere. > All the rest could be done using cylinder. > The middle could be a cube. > The second from right could be a sphere. Right. Right. Wrong. Right. -- View this message in context: http://forum.openscad.org/Newbie-with-rotation-problem-tp16873p16914.html Sent from the OpenSCAD mailing list archive at Nabble.com.

Ronaldo

Mon, Apr 4, 2016 3:33 AM

The quiz answer:

translate([-40,0,0]) cylinder(r1=20,r2=0,h=25,$fn=3);
translate([0,0,13]) sphere(15,$fa=180);
translate([35,0,0]) cylinder(r=10*sqrt(2),h=20,$fn=4);
translate([70,0,10]) sphere(15,$fn=3);
translate([105,0,9]) sphere(15,$fn=4);

Although I used spheres in the last two, the same result could be made with
cylinder as dough pointed out.
But, the middle one could be not be made by a cube. Why? Cubes are aligned
with the axis and cylinder starts the base discretization at the x axis.
Well, there were no axis in the image. Yes, but there are two clues of their
directions: the other cylinders and the frame! The frame were made by very
elongated cubes:

translate([-60,-35,-10]) cube([190,0.5,0.5]);
translate([130,-35,-10]) cube([0.5, 70,0.5]);
translate([-60, 35,-10]) cube([190,0.5,0.5]);
translate([-60,-35,-10]) cube([0.5, 70,0.5]);

translate([-60,-35,30]) cube([190,0.5,0.5]);
translate([130,-35,30]) cube([0.5, 70,0.5]);
translate([-60, 35,30]) cube([190,0.5,0.5]);
translate([-60,-35,30]) cube([0.5, 70,0.5]);

translate([-60,-35,-10]) cube([0.5, 0.5,40]);
translate([130, 35,-10]) cube([0.5, 0.5,40]);
translate([-60, 35,-10]) cube([0.5, 0.5,40]);
translate([130,-35,-10]) cube([0.5, 0.5,40]);

so they are aligned with the axis. I could not made them with cylinders
without rotations or scale.

To redeem myself, here is something useful. I have been using those "lines"
a lot to display drawings of polygonals (curves) and meshes for debugging my
surface designs. I even have a module for this:

// p0, p1 points in 3D, thickness number, dots boolean
module line(p0, p1, thickness=1, dots=false) {

function transpose_3_to_4(m) =
[ [m[0][0],m[1][0],m[2][0],0],
[m[0][1],m[1][1],m[2][1],0],
[m[0][2],m[1][2],m[2][2],0],
[0, 0, 0, 1] ];

function unit(v) = v/norm(v);

function rotate_Z_to(t) =
let( t2 = unit(t),
v2 = t2 + [0,0,1],
d = v2 * v2,
d2 = d<1e-6? 1: d,
r2 = unit([1,0,0] - (2/d2) * v2[0] * v2) ,
c2 = unit(cross(r2, t2)))
transpose_3_to_4([ r2, c2, t2 ]);

if (dots) {
translate(p0)
cube(thickness, center=true);
} else {
w = p1-p0;
if (norm(w)>1e-3) {
translate(p0)
multmatrix(rotate_Z_to(w))
cylinder(d=thickness, h=norm(w), $fn=4);
}
}
}

I could have used cube instead of cylinder in that module. If you draw a lot
of polygonals with that, render may expend a lot of time to calculate their
tiny intersection. I use it just for preview.

--
View this message in context: http://forum.openscad.org/Newbie-with-rotation-problem-tp16873p16948.html
Sent from the OpenSCAD mailing list archive at Nabble.com.

The quiz answer: translate([-40,0,0]) cylinder(r1=20,r2=0,h=25,$fn=3); translate([0,0,13]) sphere(15,$fa=180); translate([35,0,0]) cylinder(r=10*sqrt(2),h=20,$fn=4); translate([70,0,10]) sphere(15,$fn=3); translate([105,0,9]) sphere(15,$fn=4); Although I used spheres in the last two, the same result could be made with cylinder as dough pointed out. But, the middle one could be not be made by a cube. Why? Cubes are aligned with the axis and cylinder starts the base discretization at the x axis. Well, there were no axis in the image. Yes, but there are two clues of their directions: the other cylinders and the frame! The frame were made by very elongated cubes: translate([-60,-35,-10]) cube([190,0.5,0.5]); translate([130,-35,-10]) cube([0.5, 70,0.5]); translate([-60, 35,-10]) cube([190,0.5,0.5]); translate([-60,-35,-10]) cube([0.5, 70,0.5]); translate([-60,-35,30]) cube([190,0.5,0.5]); translate([130,-35,30]) cube([0.5, 70,0.5]); translate([-60, 35,30]) cube([190,0.5,0.5]); translate([-60,-35,30]) cube([0.5, 70,0.5]); translate([-60,-35,-10]) cube([0.5, 0.5,40]); translate([130, 35,-10]) cube([0.5, 0.5,40]); translate([-60, 35,-10]) cube([0.5, 0.5,40]); translate([130,-35,-10]) cube([0.5, 0.5,40]); so they are aligned with the axis. I could not made them with cylinders without rotations or scale. To redeem myself, here is something useful. I have been using those "lines" a lot to display drawings of polygonals (curves) and meshes for debugging my surface designs. I even have a module for this: // p0, p1 points in 3D, thickness number, dots boolean module line(p0, p1, thickness=1, dots=false) { function transpose_3_to_4(m) = [ [m[0][0],m[1][0],m[2][0],0], [m[0][1],m[1][1],m[2][1],0], [m[0][2],m[1][2],m[2][2],0], [0, 0, 0, 1] ]; function unit(v) = v/norm(v); function rotate_Z_to(t) = let( t2 = unit(t), v2 = t2 + [0,0,1], d = v2 * v2, d2 = d<1e-6? 1: d, r2 = unit([1,0,0] - (2/d2) * v2[0] * v2) , c2 = unit(cross(r2, t2))) transpose_3_to_4([ r2, c2, t2 ]); if (dots) { translate(p0) cube(thickness, center=true); } else { w = p1-p0; if (norm(w)>1e-3) { translate(p0) multmatrix(rotate_Z_to(w)) cylinder(d=thickness, h=norm(w), $fn=4); } } } I could have used cube instead of cylinder in that module. If you draw a lot of polygonals with that, render may expend a lot of time to calculate their tiny intersection. I use it just for preview. -- View this message in context: http://forum.openscad.org/Newbie-with-rotation-problem-tp16873p16948.html Sent from the OpenSCAD mailing list archive at Nabble.com.