How to create a streamplot only inside a polygon?

New to Julia
1

Say I got a triangle defined by

using CairoMakie, GeometryBasics, DelaunayTriangulation

P =  [(-1,0),(1,0),(0,1),(-1,0)]

Now let’s triangulate the triangle to get equal points (x,y) indside

boundary_nodes, points = convert_boundary_points_to_indices(P)

tri = DelaunayTriangulation.triangulate(points)

refine!(tri; max_area=1e-2get_total_area(tri))


pts = [Point(val[1], val[2]) for val in tri.points]
fcs = [TriangleFace(val[1], val[2], val[3]) for val in tri.triangles]


msh = GeometryBasics.Mesh(pts, fcs)


x = [val[1] for val in tri.points]

y = [val[2] for val in tri.points]

Finally let’s just define a test-function f that assigns a value based on the point (x,y)

f(x,y) = Point2f(x,y)

After all If I run

streamplot(f, x, y)

I get streamlines also outside of the triangle even if x and y are points only from the inside.

streamovertri
streamovertri1200×900 298 KB

Is there a way to restrict the lines so that they don’t reach outside? This would help me tremendously with my project. Cheers!

2

Well…you can’t really restrict the lines easily, but what you can do is plot a white polygon with a triangular hole over the plot.

Consider something like:

fx(x,y) = Point2f(x,y)
f, a, p = streamplot(fx, -1..1, 0..1)
tri = Point2f[(-1,0),(1,0),(0,1),(-1,0)]
out = Rect(-5, -5, 10, 10)
mask_poly = Makie.GeometryBasics.Polygon(
           Makie.convert_arguments(Makie.PointBased(), out)[1], # convert the rectangle to a vector of points
           [tri]
 )
poly!(a, mask_poly; color = :white, xautolimits = false, yautolimits = false) # so that the mask does not interfere with the limits

translate!(a.scene, 0, 0, -100) # move the plots below the grid so the grid is seen!
f

Unfortunately Discourse isn’t letting me upload an image, but this worked sufficiently on my machine!

1 Like
3

Alright thank you :smile: This may be the easiest solution. Modifying the streamplot-code so that it adapt to boundaries might take way too much effort.