adding roundcorner

Author: cormullion

CHANGELOG.md

@@ -1,11 +1,15 @@
 # Changelog
 
-## [v4.4] - forthcoming
+## [v4.4] - 2025-11-08
 
 ### Added
 
+- roundcorner()
+
 ### Changed
 
+- compat entries
+
 ### Removed
 
 ### Deprecated

Project.toml

@@ -32,7 +32,7 @@ Aqua = "0.8"
 Base64 = "1.6"
 Cairo = "1.0, 1.1"
 Colors = "0.11, 0.12, 0.13"
-DataStructures = "0.18, 0.19"
+DataStructures = "0.19"
 Dates = "1.6"
 FFMPEG = "^0.4.1"
 FileIO = "1"

docs/src/howto/geometrytools.md

@@ -177,6 +177,38 @@ nothing # hide
 
 ![angle three points](../assets/figures/anglethreepoints.png)
 
+## Round corners
+
+The [`roundcorner`](@ref) function takes three points that define a corner, plus a radius. The function returns three points and a Boolean flag: the first and third define the ends of the circular arc, the second defines the center of the circle with the given radius. The Boolean flag indicates whether the arc should be drawn clockwise.
+
+```@example
+using Luxor # hide
+@drawsvg begin # hide
+    background(0.8, 0.7, 0.7)
+    fontsize(25)
+    
+    p1, corner, p3 = ngon(O, 250, 3, vertices=true)
+    
+    label.(("p1", "corner", "p3"), :NE, (p1, corner, p3))
+    circle.((p1, corner, p3), 5, :fill)
+    
+    p1c, cp, p2c, clockwise = roundcorner(p1, corner, p3, 80)
+    
+    label.(("p1c", "cp", "p2c"), :NW, (p1c, cp, p2c))
+    circle.((p1c, cp, p2c), 5, :fill)
+
+    @layer begin setdash("dot"); circle(cp, 80, :stroke) end
+
+    move(p1)
+    line(p1c)
+    arc2r(cp, p1c, p2c)
+    line(p3)
+    strokepath()
+end 800 600 # hide
+```
+
+## Other functions
+
 Other functions that help with geometry include:
 
 - [`distance`](@ref) distance between two points

src/Luxor.jl

@@ -112,7 +112,7 @@ export Drawing,
     ellipseinquad, crescent, ngon, ngonside, star, pie, polycross,
     do_action, paint, paint_with_alpha, fillstroke, AbstractPoint, Point, O, randompoint, randompointarray, midpoint,
     between, slope, intersectionlines, pointlinedistance,
-    getnearestpointonline, isinside,
+    getnearestpointonline, isinside, roundcorner, 
     rotatepoint, perpendicular, crossproduct,
     dotproduct, determinant3, distance, prettypoly, polysmooth, polysplit,
     poly, simplify, polycentroid, polysortbyangle, polyhull,

src/polygons.jl

@@ -417,6 +417,92 @@ end
 polysmooth(points::Vector{Point}, radius; action = :none, debug = false, close = true) =
     polysmooth(points, radius, action; debug = debug, close = close)
 
+"""
+    roundcorner(p1::Point, cornerpoint::Point, p2::Point, radius)
+
+Given a corner `cornerpoint` defined by the three points `p1`, `cornerpoint`, and `p2`,
+calculate the intersection points and centerpoint for a smooth rounded corner. 
+    
+Returns
+    
+    `p1_cross`, `circlepoint`, `p2_cross`, `clockwise`
+    
+The corner can be drawn as:
+
+    p1 -> p1_cross -> arc2r(circlepoint, p1_cross, p2_cross) -> p2_cross -> p2
+
+`clockwise` is true if the arc is to drawn clockwise.
+"""
+function roundcorner(p1::Point, cornerpoint::Point, p2::Point, radius)
+    if isapprox(radius, 0.0)
+		throw(error("roundcorner: impossibly small radius $radius"))
+	end
+    dx1 = cornerpoint.x - p1.x     # vector 1
+    dy1 = cornerpoint.y - p1.y
+    dx2 = cornerpoint.x - p2.x     # vector 2
+    dy2 = cornerpoint.y - p2.y
+
+    # Angle between vector 1 and vector 2 divided by 2
+    angle2 = (atan(dy1, dx1) - atan(dy2, dx2)) / 2
+
+    #  length of segment between corner point and the
+    #  points of intersection with the circle of a given radius
+    t = abs(tan(angle2))
+    segment = radius / t
+
+    # Check the segment
+    length1 = hypot(dx1, dy1)
+    length2 = hypot(dx2, dy2)
+    seglength = min(length1, length2)
+    if segment > seglength
+        segment = seglength
+        radius = seglength * t
+    end
+
+    #  points of intersection are calculated by the proportion between
+    #  the coordinates of the vector, length of vector and the length of the segment.
+    p1_cross = Luxor.getproportionpoint(cornerpoint, segment, length1, dx1, dy1)
+    p2_cross = Luxor.getproportionpoint(cornerpoint, segment, length2, dx2, dy2)
+
+    #  calculation of the coordinates of the circle's center by the addition of angular vectors
+    dx = cornerpoint.x * 2 - p1_cross.x - p2_cross.x
+    dy = cornerpoint.y * 2 - p1_cross.y - p2_cross.y
+    L = hypot(dx, dy)
+    d = hypot(segment, radius)
+    # this prevents impossible constructions; Cairo will crash if L is 0
+    if isapprox(L, 0.0)
+        L = 0.01
+    end
+    circlepoint = Luxor.getproportionpoint(cornerpoint, d, L, dx, dy)
+
+    # start angle and end engle of arc
+    startangle = atan(p1_cross.y - circlepoint.y, p1_cross.x - circlepoint.x)
+    endangle = atan(p2_cross.y - circlepoint.y, p2_cross.x - circlepoint.x)
+
+    if endangle < 0
+        endangle = 2π + endangle
+    end
+    if startangle < 0
+        startangle = 2π + startangle
+    end
+    sweepangle = endangle - startangle
+
+    if abs(sweepangle) > π
+        if startangle < endangle
+            clockwise = false
+        else
+            clockwise = true
+        end
+    else
+        if startangle < endangle
+            clockwise = true
+        else
+            clockwise = false
+        end
+    end
+    return p1_cross, circlepoint, p2_cross, clockwise
+end
+
 """
     offsetpoly(plist::Vector{Point}, d::T) where T<:Number
 

test/round-corner-test.jl

@@ -0,0 +1,40 @@
+using Luxor
+using Test
+using Random
+Random.seed!(42)
+
+function test_roundcorner(fname)
+    @draw begin
+        p1, p2, p3 = ngon(O, 100, 3, vertices = true)
+        s, cp, f = roundcorner(p1, p2, p3, 50)
+        line(p1, s, :stroke)
+        line(f, p3, :stroke)
+        arc2r(cp, s, f, :stroke)
+
+        @test ispointonline(s, p1, p2) == true
+        @test ispointonline(f, p2, p3) == true
+    end
+
+    return Drawing(700, 700, fname)
+    background("black")
+    origin()
+        setline(1)
+        bx = ngon(O, 250, 4, vertices = true)
+        for radius in 0.0000001:10:400
+            for (n, pt) in enumerate(bx)
+                randomhue()
+                p1 = bx[mod1(n - 1, end)]
+                p2 = bx[mod1(n, end)]
+                p3 = bx[mod1(n + 1, end)]
+                startc, centerp, endc, flag = roundcorner(
+                    p1, p2, p3, radius
+                )
+                arc2r(centerp, startc, endc, :stroke)
+            end
+        end
+    @test finish() == true
+    println("...finished test: output in $(fname)")
+end
+
+test_roundcorner("round-corner-test-1.png")
+println("...finished roundcorner test")

test/runtests.jl

@@ -96,6 +96,7 @@ function run_all_tests()
         include("arc-sagitta-test.jl")
         include("circlecircletangent-test.jl")
         include("crescent-test.jl")
+        include("round-corner-test.jl")
     end
 
     @testset "color" begin