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Fixing trigonometry

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Ajabep 2026-01-14 21:45:32 +01:00
commit 9bebad59c3
1 changed files with 38 additions and 12 deletions
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c3cat-bottle-clip/c3cat-bottle-clip.scad
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@ -480,24 +480,50 @@ module ear(depth, thickness, side_len=30, bend_factor=0.5, stretch_factor=1.2, c
depth = depth == undef ? 20 : depth ;
thickness = thickness == undef ? 3 : thickness ;
echo("Generating ONE single ear",
depth = depth,
thickness = thickness,
side_len = side_len,
bend_factor = bend_factor,
stretch_factor = stretch_factor,
chamfer = chamfer,
chamfer_shape = chamfer_shape,
details = details
);
// $A and $B are the end of the ear
// $C is the higher end point.
$A=[0, side_len/2];
$B=[0,-side_len/2];
$C=[-(side_len/2/sin(120))*1.5*stretch_factor, 0];
// From the front, an ear looks like:
//
// $C
// /|\
// / | \
// / | \
// /---+---\
// $B c $A
//
// c is the origin of the ear.
// $Bc$C and $Ac$C are 90deg angles.
//
// The length [$B $A] is `side_len`
// Thus, [$B c] == [c $A] == side_len/2
//
// Since SOH, sin(angle) = Opposed / Hypotenuse
// sin(angle) = Opposed / Hypotenuse
// sin(angle) * Hypotenuse = Opposed
// Hypotenuse = Opposed / sin(angle)
//
// Thus, the `(side_len/2/sin(120))` implies that "The opposed side of the 120 angle is `(side_len/2)` length" and is the formula to know the size of the hypotenuse.
// Moreover, a 120deg angle in a right rectangle does not exists: the sum of all the angles of a triangle needs to be 180deg. I think the author tried, instead, to use the 60 as an angle, since the sinus is the same.
//
// The correct formula should be `((side_len/2)*tan(60))`: since $C$B$A should a 60deg angle to have an equilateral `$A$B$C` triangle, the product of the tangent ("TOA") of this angle and the adjacent segment [$B c] will give us the size of length of the opposed segment [$C c].
//
// MOREOVER, the product of the magic number `1.5` with the divisor `sin(120)`... is actually the result of the `tan(60)`!
//
// The original formula was:
// $C=[-(side_len/2/sin(120))*1.5*stretch_factor, 0];
$C=[-((side_len/2)*tan(60))*stretch_factor, 0];
// $a, $b and $c are the distance between the different points of the triangle.
$c=sqrt(pow($A.x-$B.x, 2)+pow($A.y-$B.y, 2));
$b=sqrt(pow($A.x-$C.x, 2)+pow($A.y-$C.y, 2));
$a=sqrt(pow($C.x-$B.x, 2)+pow($C.y-$B.y, 2));
// $hc is the height of $C.
$hc=-$C.x;
// If I correctly understood, $alpha should be the angle of the $B$A$C. This should be 60deg... but is not. idk why.
$alpha=asin($hc/$b);
$beta=$alpha;
$gamma=180-$alpha-$beta;