# ParametricPlot with variable range

I want to plot a triangle like

(not exactly, it is a simplified version) using points (x,y) with 0 < x < y in the range 1<y<0. It would be nice if the following works but not.

ParametricPlot[{x, y}, {x, 0, y}, {y, 0, 1}]


Something close to it can be done by

ParametricPlot[{x, y}&&(x<y), {x, 0, 1}, {y, 0, 1}]


but I obtain a wiggly triangle.

Do you have any solution?

• ParametricPlot[{y, y - x}, {x, 1, 0}, {y, 0, x}]
– Acus
Commented Jun 11, 2021 at 7:54
• ParametricPlot[{x y, y}, {x, 0, 1}, {y, 0, 1}]?
– kglr
Commented Jun 11, 2021 at 8:03
• ParametricPlot[{x, y} && (x<y) ... I have never seen this syntax. Where did you learn it? Commented Jun 11, 2021 at 8:22
• Are you sure you don't want RegionPlot instead of ParametricPlot? If not, can you explain why? Additionally: most plotting functions in Mathematica have a RegionFunction option which can be used to restrict the plotting region to arbitrary shaped. It is especially useful with DensityPlot and similar functions. The arguments it takes are different for each plotting function—look them up! Commented Jun 11, 2021 at 8:25
• @Szabolcs Thank you for the hint, but this is a simplified version of my problem, whose space is not the same as the range. Commented Jun 11, 2021 at 13:34

reg = ParametricRegion[{{x, y}, x < y}, {{x, 0, 1}, {y, 0, 1}}];
HighlightMesh[
BoundaryDiscretizeRegion[
reg], {Style[1, Directive[Thickness[.03], Red]], Style[2, None]},


reg = ParametricRegion[{{x, y}, x < y}, {{x, 0, 1}, {y, 0, 1}}];
RegionPlot[RegionBoundary[DiscretizeRegion[reg]],
BoundaryStyle -> Directive[Thickness[.03], Red],

ParametricPlot[{x, y}, {y, 0, 1}, {x, 0, y}, PlotStyle -> None,