Simple trigonometry problem (I think I should go back to school)

> Hello,
>
> It has been a while since I touched OpenScad. I'm starting from
> scratch once again, I forgot everything.
> I'm trying to "design" simple brackets and drill templates for PCBs.
> Following
> https://hackaday.com/2018/02/13/openscad-tieing-it-together-with-hull/
>  precepts, I define my points, make cylinders, holes and then hull to
> stitch everything together.
> The problem I'm facing right now is that I get my trigo wrong. I don't
> think it's OpenScad, it's maybe a bad understanding of what I'm
> supposed to do with the atan function.
> I have four holes, forming a rectangle. I have then four feets. I'm
> trying to join 2 feet by a diagonal cylinder. So I'm dividing the
> opposite side by the adjacent side, and applying atan() on the result,
> to hopefully find the angle I'm supposed to use in rotate().
> Unfortunately, that does not fit correctly, I'm a few degrees wrong.
> I know it's stupid and I'm rusted with OpenScad and trigonometry, but
> if anyone could point me in the right direction, that could help.
>
> Thanks in advance,
>
>
> feet = [[0,0,0], [42.11,0,0], [0,40.11,0], [42.11,40.11,0]];
> holeSize = 3;
> baseSize = 9;
> footSize = 5;
> baseHeight = 3;
> totalHeight = 7;
> linkThickness = 3;
> linkHeight = 2;
>
> feet(feet,holeSize, baseSize, baseHeight, totalHeight);
> link(feet, linkThickness, linkHeight);
>
> module foot(point, holeSize, baseSize, baseHeight, totalHeight) {
>     difference() {
>       union()  {
>             hull() {
>                 cylinder(r=baseSize/2, h=baseHeight, $fn=100);
>                 translate([0,0,(totalHeight - baseHeight)/2])
> cylinder(r=footSize/2, h=baseHeight, $fn=100);
>             }
>             translate([0,0,totalHeight - baseHeight])
> cylinder(r=footSize/2, h=baseHeight, $fn=100);
>         }
>         color("red") translate([0,0,-0.5]) cylinder(r=holeSize/2,
> h=totalHeight+1, $fn=100);
>     }
>  }
>
>  module feet(points,holeSize, baseSize, baseHeight, totalHeight) {
>      for (point = points) {
>          translate (point) foot(point, holeSize, baseSize, baseHeight,
> totalHeight);
>      }
>  }
>
>  module link(points, thickness, height) {
>      firstSide = points[1][0] - points[0][0];
>      secondSide = points[3][1] - points[0][0];
>      length = sqrt(pow(firstSide,2) + pow(secondSide,2));
>      tan = secondSide/firstSide;
>      atan = atan(secondSide/firstSide);
>      echo ("tan is", tan, " and atan is ", atan);
>      //360-atan(tan)
>      color("blue") translate([0,0,height*2]) rotate([270,0,-atan])
> cylinder(h=length, r=thickness/2, center=false, $fn=100);
>  }
> --
> Bruno Verachten
>
> _______________________________________________
> OpenSCAD mailing list

>
> Another method not involving atan (or a library) (I think quaternions are
> easier):
>
> feet = [[0,0,0], [42.11,0,0], [0,40.11,0], [42.11,40.11,0]];
> holeSize = 3;
> baseSize = 9;
> footSize = 5;
> baseHeight = 3;
> totalHeight = 7;
> linkThickness = 3;
> linkHeight = 2;
>
> feet(feet,holeSize, baseSize, baseHeight, totalHeight);
> link(feet, linkThickness, linkHeight);
>
> module foot(point, holeSize, baseSize, baseHeight, totalHeight) {
>     difference() {
>       union()  {
>             hull() {
>                 cylinder(r=baseSize/2, h=baseHeight, $fn=100);
>                 translate([0,0,(totalHeight - baseHeight)/2])
> cylinder(r=footSize/2, h=baseHeight, $fn=100);
>             }
>             translate([0,0,totalHeight - baseHeight])
> cylinder(r=footSize/2, h=baseHeight, $fn=100);
>         }
>         color("red") translate([0,0,-0.5]) cylinder(r=holeSize/2,
> h=totalHeight+1, $fn=100);
>     }
>  }
>
>  module feet(points,holeSize, baseSize, baseHeight, totalHeight) {
>      for (point = points) {
>          translate (point) foot(point, holeSize, baseSize, baseHeight,
> totalHeight);
>      }
>  }
>
>  module link(points, thickness, height) {
>      firstSide = points[1][0] - points[0][0];
>      secondSide = points[3][1] - points[0][0];
>      length = sqrt(pow(firstSide,2) + pow(secondSide,2));
>      tan = secondSide/firstSide;
>      atan = atan(secondSide/firstSide);
>      echo ("tan is", tan, " and atan is ", atan);
>      //360-atan(tan)
>      color("blue")
>      translate([0,0,height*2])
>      rotate(-90, [secondSide/length, -firstSide/length, 0])
> cylinder(h=length, r=thickness/2, center=false, $fn=100);
>  }
>
>
>
>
> --
> Sent from: http://forum.openscad.org/
>
> _______________________________________________
> OpenSCAD mailing list
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> http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

> On 2020-11-26 16:17, Verachten Bruno wrote:
>> I have four holes, forming a rectangle. I have then four feets. I'm
>> trying to join 2 feet by a diagonal cylinder. So I'm dividing the
>> opposite side by the adjacent side, and applying atan() on the result,
>> to hopefully find the angle I'm supposed to use in rotate().
>> Unfortunately, that does not fit correctly, I'm a few degrees wrong.
>
> There is no need to use trigonometric functions for something like
> this. Try this to replace your link
>
> module link(points, thickness, height) {
>     pdx = points[3][0] - points[0][0];
>     pdy = points[3][1] - points[0][1];
>     length = sqrt(pow(pdx,2) + pow(pdy,2));
>     dx = pdx/length;
>     dy = pdy/length;
>     color("blue")
>     translate([0,0,height*2])
>     multmatrix([[dx,-dy,0,0],[dy,dx,0,0],[0,0,1,0],[0,0,0,1]])
>     rotate([0,90,0])
>     cylinder(h=length, r=thickness/2, center=false, $fn=100);
> }