Method and device for rendering areas bounded by curves using a GPU

A method of rendering pixels, comprising:

• retrieving, from a memory of a computing device, a graphics model, the graphics model comprising parameters of Bézier curves having at most four control points, a simple Bézier arch obtainable using the parameters;
• when a Bézier curve of the graphics model is not a simple Bézier arch, subdividing the Bézier curve into simple Bézier arches;
• for each simple Bézier arch defined by a control sequence consisting of (a) an initial endpoint E1, followed by (b) either (i) a single attraction point Co or (ii) a first attraction point C1 followed by a second attraction point C2, followed by (c) a terminal endpoint E2, at least one attraction point being non-co-linear with the endpoints:
• determining, using a pre-processing program executable by a central processing unit of the computing device, a domain triangle containing the arch and having as vertices E1, E2, and an intersection point I of rays emanating from the endpoints and passing through respective attraction points associated with the endpoints;
• and
• for each pixel in the domain triangle:
• computing, using a shader program executable by a graphics processing unit of the computing device, a value of a function f(τ0, τ1, τ2, d1, d2)=τ0τ2d1+τ12d2, wherein τ0, τ1, τ2 are barycentric co-ordinates of that pixel, based on E1, and E2, respectively;
• wherein d1 and d2 are each linear functions of τ0, τ1, and τ2;
• and wherein the function evaluates to zero if that pixel is on the arch;
• and
• rendering, using the graphics processing unit in communication with the central processing unit, that pixel based on the computed value, the graphics processing unit being directed by the shader program;
• wherein rendering that pixel comprises rendering to one or more of:
• a display device, a file in the memory and a peripheral device.