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rounded_polygon() now copes with the degenrate case when tangents intersect to form a sharp corner with no arc.

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Added an offset() function with some limitations.
This commit is contained in:
Chris Palmer 2022-06-21 12:29:57 +01:00
parent 1ddfb35bda
commit 28c36a4e96
2 changed files with 43 additions and 13 deletions
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2
readme.md
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@ -6608,6 +6608,8 @@ Because the tangents need to be calculated to find the length these can be calcu
| Function | Description |
|:--- |:--- |
| `circle_tangent(p1, p2)` | Compute the clockwise tangent between two circles represented as [x,y,r] |
| `line_intersection(l0, l1)` | Return the point where two 2D lines intersect or undef if they don't. |
| `offset(points, offset)` | Offset a 2D polygon, breaks for concave shapes and negative offsets if the offset is more than half the smallest feature size. |
| `rounded_polygon(points, _tangents = undef)` | Return the rounded polygon from the point list, can pass the tangent list to save it being calculated |
| `rounded_polygon_arcs(points, tangents)` | Compute the arcs at the points, for each point [angle, rotate_angle, length] |
| `rounded_polygon_length(points, tangents)` | Calculate the length given the point list and the list of tangents computed by `rounded_polygon_tangents` |

54
utils/rounded_polygon.scad
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@ -33,7 +33,7 @@ function circle_tangent(p1, p2) = //! Compute the clockwise tangent between two
dx = p2.x - p1.x,
dy = p2.y - p1.y,
d = sqrt(dx * dx + dy * dy),
theta = atan2(dy, dx) + acos((r1 - r2) / d),
theta = assert(d, str("points conicident ", p1)) atan2(dy, dx) + acos((r1 - r2) / d),
v = [cos(theta), sin(theta)]
)[ p1 + r1 * v, p2 + r2 * v ];
@ -72,24 +72,52 @@ function rounded_polygon_length(points, tangents) = //! Calculate the length giv
arcs = rounded_polygon_arcs(points, tangents)
) sumv( map( concat(tangents, arcs), function(e) e[2] ) );
function line_intersection(l0, l1) = //! Return the point where two 2D lines intersect or undef if they don't.
assert(Len(l0) == 2 && Len(l1) == 2, "Two 2D vectors expected")
let(
p0 = l0[0], p1 = l0[1], p2 = l1[0], p3 = l1[1],
v1 = p1 - p0,
v2 = p3 - p2,
v3 = p0 - p2,
det = v1.x * v2.y - v2.x * v1.y,
s = det ? (-v1.y * v3.x + v1.x * v3.y) / det : inf,
t = det ? ( v2.x * v3.y - v2.y * v3.x) / det : inf
) s >= 0 && s <= 1 && t >= 0 && t <= 1 ? p0 + t * v1 : undef;
function rounded_polygon(points, _tangents = undef) = //! Return the rounded polygon from the point list, can pass the tangent list to save it being calculated
let(
len = len(points),
tangents = _tangents ? _tangents : rounded_polygon_tangents(points),
arcs = rounded_polygon_arcs(points, tangents)
) [for(i = [0 : len - 1], last = (i - 1 + len) % len, R = points[i][2]) each [
vec2(tangents[last][1]), // End of last tangent
if(R) // If rounded
let(r = abs(R), // Get radius
n = r2sides4n(r), // Decide number of vertices
step = 360 / n, // Angular step
arc = arcs[i], // Get corner arc details
start = ceil(arc[1] / step + eps), // Starting index
end = floor((arc[0] + arc[1]) / step - eps), // Ending index
c = vec2(points[i]) // Centre of arc
) for(j = R > 0 ? [end : -1 : start] : [start : 1 : end], a = j * step) c + r * [cos(a), sin(a)], // Points on the arc
vec2(tangents[i][0])] // Start of next tangent
) [for(i = [0 : len - 1], last = (i - 1 + len) % len)
let(
t0 = vec2(tangents[last]),
t1 = vec2(tangents[i]),
p = line_intersection(t0, t1), // Do the tangents cross?
R = points[i][2]
)
if(!is_undef(p)) // Tangents intersect, so just add the intersection point
p
else
each [ // Else link the two tangent ends with an arc
t0[1], // End of last tangent
if(R) // If rounded
let(r = abs(R), // Get radius
n = r2sides4n(r), // Decide number of vertices
step = 360 / n, // Angular step
arc = arcs[i], // Get corner arc details
start = ceil(arc[1] / step + eps), // Starting index
end = floor((arc[0] + arc[1]) / step - eps), // Ending index
c = vec2(points[i]) // Centre of arc
) for(j = R > 0 ? [end : -1 : start] : [start : 1 : end], a = j * step)
c + r * [cos(a), sin(a)], // Points on the arc
if(R)
t1[0], // Start of next tangent
]
];
function offset(points, offset) = //! Offset a 2D polygon, breaks for concave shapes and negative offsets if the offset is more than half the smallest feature size.
rounded_polygon([for(p = points) [p.x, p.y, offset]]);
module rounded_polygon(points, _tangents = undef) //! Draw the rounded polygon from the point list, can pass the tangent list to save it being calculated
polygon(rounded_polygon(points, _tangents), convexity = len(points));