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https://github.com/revarbat/BOSL2.git
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Added convex_hull()
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Revar Desmera
264
math.scad
264
math.scad
@@ -44,6 +44,8 @@ include <compat.scad>
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PHI = (1+sqrt(5))/2; // The golden ratio phi.
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EPSILON = 1e-9; // A really small value useful in comparing FP numbers. ie: abs(a-b)<EPSILON
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// Function: Cpi()
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@@ -94,6 +96,36 @@ function quantup(x,y) = ceil(x/y)*y;
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function constrain(v, minval, maxval) = min(maxval, max(minval, v));
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// Function: min_index()
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// Usage:
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// min_index(vals);
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// Description:
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// Returns the index of the minimal value in the given list.
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function min_index(vals, _minval, _minidx, _i=0) =
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_i>=len(vals)? _minidx :
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min_index(
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vals,
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((_minval == undef || vals[_i] < _minval)? vals[_i] : _minval),
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((_minval == undef || vals[_i] < _minval)? _i : _minidx),
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_i+1
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);
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// Function: max_index()
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// Usage:
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// max_index(vals);
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// Description:
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// Returns the index of the maximum value in the given list.
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function max_index(vals, _maxval, _maxidx, _i=0) =
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_i>=len(vals)? _maxidx :
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max_index(
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vals,
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((_maxval == undef || vals[_i] > _maxval)? vals[_i] : _maxval),
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((_maxval == undef || vals[_i] > _maxval)? _i : _maxidx),
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_i+1
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);
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// Function: posmod()
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// Usage:
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// posmod(x,m)
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@@ -788,6 +820,20 @@ function unique(arr) =
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// Function: list_remove()
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// Usage:
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// list_remove(list, elements)
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// Description:
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// Remove all items from `list` whose indexes are in `elements`.
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// Arguments:
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// list = The list to remove items from.
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// elements = The list of indexes of items to remove.
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function list_remove(list, elements) = [
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for (i = [0:len(list)-1]) if (!search(i, elements)) list[i]
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];
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// Internal. Not exposed.
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function _array_dim_recurse(v) =
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!is_list(v[0])? (
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@@ -1114,6 +1160,42 @@ function xy_to_polar(x,y=undef) = let(
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) [norm([xx,yy]), atan2(yy,xx)];
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// Function: xyz_to_planar()
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// Usage:
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// xyz_to_planar(point, a, b, c);
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// Description:
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// Given three points defining a plane, returns the projected planar
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// [X,Y] coordinates of the closest point to a 3D `point`. The origin
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// of the planar coordinate system [0,0] will be at point `a`, and the
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// Y+ axis direction will be towards point `b`. This coordinate system
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// can be useful in taking a set of nearly coplanar points, and converting
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// them to a pure XY set of coordinates for manipulation, before convering
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// them back to the original 3D plane.
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function xyz_to_planar(point, a, b, c) = let(
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u = normalize(b-a),
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v = normalize(c-a),
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n = normalize(cross(u,v)),
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w = normalize(cross(n,u)),
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relpoint = point-a
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) [relpoint * w, relpoint * u];
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// Function: planar_to_xyz()
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// Usage:
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// planar_to_xyz(point, a, b, c);
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// Description:
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// Given three points defining a plane, converts a planar [X,Y]
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// coordinate to the actual corresponding 3D point on the plane.
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// The origin of the planar coordinate system [0,0] will be at point
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// `a`, and the Y+ axis direction will be towards point `b`.
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function planar_to_xyz(point, a, b, c) = let(
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u = normalize(b-a),
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v = normalize(c-a),
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n = normalize(cross(u,v)),
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w = normalize(cross(n,u))
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) a + point.x * w + point.y * u;
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// Function: cylindrical_to_xyz()
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// Usage:
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// cylindrical_to_xyz(r, theta, z)
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@@ -1618,4 +1700,186 @@ function pointlist_bounds(pts) = [
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];
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// Function: triangle_area2d()
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// Usage:
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// triangle_area2d(a,b,c);
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// Description:
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// Returns the area of a triangle formed between three vertices.
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// Result will be negative if the points are in clockwise order.
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// Examples:
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// triangle_area2d([0,0], [5,10], [10,0]); // Returns -50
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// triangle_area2d([10,0], [5,10], [0,0]); // Returns 50
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function triangle_area2d(a,b,c) =
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(
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a.x * (b.y - c.y) +
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b.x * (c.y - a.y) +
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c.x * (a.y - b.y)
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) / 2;
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// Function: right_of_line2d()
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// Usage:
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// right_of_line2d(line, pt)
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// Description:
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// Returns true if the given point is to the left of the given line.
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// Arguments:
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// line = A list of two points.
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// pt = The point to test.
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function right_of_line2d(line, pt) =
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triangle_area2d(line[0], line[1], pt) < 0;
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// Function: collinear()
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// Usage:
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// collinear(a, b, c, [eps]);
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// Description:
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// Returns true if three points are co-linear.
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// Arguments:
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// a = First point.
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// b = Second point.
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// c = Third point.
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// eps = Acceptable max angle variance. Default: EPSILON (1e-9) degrees.
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function collinear(a, b, c, eps=EPSILON) =
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abs(vector_angle(b-a,c-a)) < eps;
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// Function: collinear_indexed()
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// Usage:
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// collinear_indexed(points, a, b, c, [eps]);
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// Description:
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// Returns true if three points are co-linear.
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// Arguments:
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// points = A list of points.
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// a = Index in `points` of first point.
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// b = Index in `points` of second point.
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// c = Index in `points` of third point.
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// eps = Acceptable max angle variance. Default: EPSILON (1e-9) degrees.
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function collinear_indexed(points, a, b, c, eps=EPSILON) =
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let(
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p1=points[a],
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p2=points[b],
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p3=points[c]
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) abs(vector_angle(p2-p1,p3-p1)) < eps;
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// Function: plane3pt()
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// Usage:
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// plane3pt(p1, p2, p3);
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// Description:
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// Generates the cartesian equation of a plane from three non-colinear points on the plane.
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// Returns [A,B,C,D] where Ax+By+Cz+D=0 is the equation of a plane.
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// Arguments:
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// p1 = The first point on the plane.
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// p2 = The second point on the plane.
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// p3 = The third point on the plane.
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function plane3pt(p1, p2, p3) =
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let(normal = normalize(cross(p3-p1, p2-p1))) concat(normal, [normal*p1]);
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// Function: plane3pt_indexed()
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// Usage:
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// plane3pt_indexed(points, i1, i2, i3);
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// Description:
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// Given a list of points, and the indexes of three of those points,
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// generates the cartesian equation of a plane that those points all
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// lie on. Requires that the three indexed points be non-collinear.
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// Returns [A,B,C,D] where Ax+By+Cz+D=0 is the equation of a plane.
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// Arguments:
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// points = A list of points.
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// i1 = The index into `points` of the first point on the plane.
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// i2 = The index into `points` of the second point on the plane.
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// i3 = The index into `points` of the third point on the plane.
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function plane3pt_indexed(points, i1, i2, i3) =
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let(
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p1 = points[i1],
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p2 = points[i2],
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p3 = points[i3],
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normal = normalize(cross(p3-p1, p2-p1))
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) concat(normal, [normal*p1]);
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// Function: distance_from_plane()
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// Usage:
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// distance_from_plane(plane, point)
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// Description:
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// Given a plane as [A,B,C,D] where the cartesian equation for that plane
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// is Ax+By+Cz+D=0, determines how far from that plane the given point is.
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// The returned distance will be positive if the point is in front of the
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// plane; on the same side of the plane as the normal of that plane points
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// towards. If the point is behind the plane, then the distance returned
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// will be negative. The normal of the plane is the same as [A,B,C].
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// Arguments:
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// plane = The [A,B,C,D] values for the equation of the plane.
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// point = The point to test.
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function distance_from_plane(plane, point) =
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[plane.x, plane.y, plane.z] * point - plane[3];
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// Function: coplanar()
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// Usage:
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// coplanar(plane, point);
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// Description:
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// Given a plane as [A,B,C,D] where the cartesian equation for that plane
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// is Ax+By+Cz+D=0, determines if the given point is on that plane.
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// Returns true if the point is on that plane.
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// Arguments:
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// plane = The [A,B,C,D] values for the equation of the plane.
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// point = The point to test.
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function coplanar(plane, point) =
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abs(distance_from_plane(plane, point)) <= EPSILON;
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// Function: in_front_of_plane()
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// Usage:
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// in_front_of_plane(plane, point);
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// Description:
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// Given a plane as [A,B,C,D] where the cartesian equation for that plane
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// is Ax+By+Cz+D=0, determines if the given point is on the side of that
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// plane that the normal points towards. The normal of the plane is the
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// same as [A,B,C].
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// Arguments:
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// plane = The [A,B,C,D] values for the equation of the plane.
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// point = The point to test.
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function in_front_of_plane(plane, point) =
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distance_from_plane(plane, point) > EPSILON;
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// Function: simplify_path()
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// Description:
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// Takes a path and removes unnecessary collinear points.
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// Usage:
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// simplify_path(path, [eps])
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// Arguments:
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// path = A list of 2D path points.
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// eps = Largest angle variance allowed. Default: EPSILON (1-e9) degrees.
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function simplify_path(path, eps=EPSILON, _a=0, _b=2, _acc=[]) =
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(_b >= len(path))? concat([path[0]], _acc, [path[len(path)-1]]) :
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simplify_path(
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path, eps,
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(collinear_indexed(path, _a, _b-1, _b, eps=eps)? _a : _b-1),
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_b+1,
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(collinear_indexed(path, _a, _b-1, _b, eps=eps)? _acc : concat(_acc, [path[_b-1]]))
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);
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// Function: simplify_path_indexed()
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// Description:
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// Takes a list of points, and a path as a list of indexes into `points`,
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// and removes all path points that are unecessarily collinear.
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// Usage:
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// simplify_path_indexed(path, eps)
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// Arguments:
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// points = A list of points.
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// path = A list of indexes into `points` that forms a path.
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// eps = Largest angle variance allowed. Default: EPSILON (1-e9) degrees.
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function simplify_path_indexed(points, path, eps=EPSILON, _a=0, _b=2, _acc=[]) =
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(_b >= len(path))? concat([path[0]], _acc, [path[len(path)-1]]) :
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simplify_path_indexed(
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points, path, eps,
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(collinear_indexed(points, path[_a], path[_b-1], path[_b], eps=eps)? _a : _b-1),
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_b+1,
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(collinear_indexed(points, path[_a], path[_b-1], path[_b], eps=eps)? _acc : concat(_acc, [path[_b-1]]))
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);
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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