Polygon rendering device

1. A polygon rendering device comprising:

a polygon division section for dividing, based on polygon data which specifies a polygon to be rendered, the polygon into a plurality of partial polygons such that at least one of the plurality of partial polygons has formed therein, from vertices thereof, a plurality of triangles which respectively share a vertex of the polygon; and

a partial polygon rendering section for performing a rendering process and, without requiring, further division of any of the plurality of partial polygons, generating partial image data which represents an image of the at least one partial polygon from partial polygon data, wherein

a plurality of partial image data represents an image of the polygon when combined,

the polygon data includes n sets of vertex coordinates P 1 to Pn of the polygon in such an order that the polygon can be rendered in one stroke in a forward direction, and

said polygon division section

selects one of the vertex coordinates P 1 to Pn of the polygon data as a reference vertex Pb (b=1, 2, . . . , n), and in the forward direction, selects a vertex Pc positioned adjacent to the reference vertex Pb and a vertex P(c+1) positioned adjacent to the vertex Pc, and a triangle ΔPb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) carries, in and on, no other vertex Pi (i=1, 2, . . . , n, and i≠b, i≠c, i≠c+1) belonging to the polygon and not yet selected, and an angle ∠Pb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) is smaller than 180 degrees,

selects, in addition to the reference vertex Pb and the vertex P(c+1), a vertex P(c+2) which is positioned adjacent to the vertex P(c+1) in the forward direction, and a triangle ΔPb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) carries no other vertex Pj (j=1, 2, . . . , n, and j≠b, j≠c, j≠c+1, j≠c+2) which belongs to the polygon and not yet selected, and an angle ΔPb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) is smaller than 180 degrees, and

generates the partial polygon data specifying at least the partial polygon formed by the reference vertex Pb, and the vertexes Pc, P(c+1), and P(c+2).

2. The polygon rendering device according to claim 1 , wherein said polygon division section

sets, when the vertex P(c+2) selected thereby satisfies a condition that the triangle ΔPb P(c+1) P(c+2) carries, in and on, no other vertex Pj, and the angle ∠Pb P(c+1) P(c+2) is smaller than 180 degrees, the vertex P(c+2) as the vertex P(c+1),

keeps selecting, until the condition is no longer satisfied, together with the reference vertex Pb and the newly-set vertex P(c+1), a new vertex P(c+2) which is positioned adjacent to the newly set vertex P(c+1), and

generates the partial polygon data which specifies the partial polygon formed by the reference vertex Pb, the vertexes Pc and P(C+1), and at least one of the vertexes P(c+2).

3. A polygon rendering method comprising;

a polygon division operation of dividing, based on polygon data which specifies a polygon to be rendered, the polygon into a plurality of partial polygons such that at least one of the plurality of partial polyvons has formed therein, from vertices thereof, a plurality of triangles which respectively share a vertex of the polygon; and

a partial polygon rendering operation of performing a rendering process and, without requiring further division of any of the plurality of partial polygons, generating partial image data which represents an image of the at least one partial polygon from partial polygon data, wherein

a plurality of partial image data represents an image of the polygon when combined,

the polygon data includes n sets of vertex coordinates P 1 to Pn of the polygon in such an order that the polygon can be rendered in one stroke in a forward direction,

said polygon division operation includes

a first selection operation of selecting one of the vertex coordinates P 1 to Pn of the polygon data as a reference vertex Pb (b=1, 2, . . . , n), and in the forward direction, selecting a vertex Pc positioned adjacent to the reference vertex Pb and a vertex P(c+1) positioned adjacent to the vertex Pc, and a triangle ΔPb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) carries, in and on, no other vertex Pi (i=1, 2, . . . , n, and i≠b, i≠c, i≠c+1) belonging to the polygon and not yet selected, and an angle ∠Pb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) is smaller than 180 degrees, and

a second selection operation of selecting, in addition to the reference vertex Pb and the vertex P(c+1), a vertex P(c+2) which is positioned adjacent to the vertex P(c+1) in the forward direction, and a triangle ΔPb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) carries no other vertex Pj (j=1, 2, . . . , n, and j≠b, j‥c, j≠c+1, j≠c+2) which belongs to the polygon and not yet selected, and an angle ∠Pb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) is smaller than 180 degrees, and

said polygon division operation generates the partial polygon data specifying at least the partial polygon formed by the reference vertex Pb, and the vertexes Pc, and P(c+1) selected in said first selection operation, and the vertex P(c+2) selected in said second selection operation.

4. The polygon rendering method according to claim 3 , wherein

said polygon division operation further includes a setting operation of setting the vertex P(c+2) to the vertex P(c+1) when the vertex P(c+2) selected in said second selection operation satisfies a condition that the triangle ΔPb P(c+1) P(c+2) carries, in and on, no other vertex Pj, and the angle ∠Pb P(c+1) P(c+2) is smaller than 180 degrees,

said second selection operation keeps selecting, until the condition is no longer satisfied, together with the reference vertex Pb selected in said first selection operation, and the vertex P(c+1) newly set in said setting operation, a new vertex P(c+2) which is positioned adjacent to the newly-set vertex P(c+1), and

said polygon division operation generates the partial polygon data which specifies the partial polygon formed by the reference vertex Pb, and the vertexes Pc and P(C+1) selected in said first selection operation, and the vertex P(c+2) selected in said second selection operation.

5. A polygon rendering program operable to instruct a processor to render a polygon, the polygon rendering program comprising:

a polygon division operation of dividing, based on polygon data which specifies a polygon to be rendered, the polygon into a plurality of partial polygons such that at least one of the plurality of partial polygons has formed therein, from vertices thereof, a plurality of triangles which respectively share a vertex of the polygons; and

a partial polygon rendering operation of performing a rendering process and, without requiring further division of any of the plurality of partial polygons, generating partial image data which represents an image of the at least one partial polygon from partial polygon data, wherein

a plurality of partial image data represents an image of the polygon when combined,

the polygon data includes n sets of vertex coordinates P 1 to Pn of the polygon in such an order that the polygon can be rendered in one stroke in a forward direction,

said polygon division operation includes

a first selection operation of selecting one of the vertex coordinates P 1 to Pn of the polygon data as a reference vertex Pb (b=1, 2, . . . , n), and in the forward direction, selecting a vertex Pc positioned adjacent to the reference vertex Pb and a vertex P(c+1) positioned adjacent to the vertex Pc, and a triangle ΔPb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) carries, in and on, no other vertex Pi (i=1, 2, . . . , n, and i≠b, i≠c, i≠+1) belonging to the polygon and not yet selected, and an angle ∠Pb Pc P(c+1) formed by the reference vertex Pb, and the vertexes Pc and P(c+1) is smaller than 180 degrees, and

a second selection operation of selecting, in addition to the reference vertex Pb and the vertex P(c+1), a vertex P(c+2) which is positioned adjacent to the vertex P(c+1) in the forward direction, and a triangle ΔPb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) carries no other vertex Pj (j=1, 2, . . . , n, and j≠b, j≠c, j≠c+1, j≠c+2) which belongs to the polygon and not yet selected, and an angle ∠Pb P(c+1) P(c+2) formed by the reference vertex Pb, and the vertexes P(c+1) and P(c+2) is smaller than 180 degrees, and

said polygon division operation generates the partial polygon data specifying at least the partial polygon formed by the reference vertex Pb, and the vertexes Pc, and P(c+1) selected in said first selection operation, and the vertex P(c+2) selected in said second selection operation.

6. The polygon rendering program according to claim 5 , wherein

said polygon division operation further includes a setting operation of setting the vertex P(c+2) to the vertex P(c+1) when the vertex P(c+2) selected in said second selection operation satisfies a condition that the triangle ΔPb P(c+1) P(c+2) carries, in and on, no other vertex Pj, and the angle ∠Pb P(c+1) P(c+2) is smaller than 180 degrees,

said second selection operation keeps selecting, until the condition is no longer satisfied, together with the reference vertex Pb selected in said first selection operation, and the vertex P(c+1) newly set in said second selection operation, a new vertex P(c+2) which is positioned adjacent to the newly set vertex P(c+1), and

said polygon division operation generates the partial polygon data which specifies the partial polygon formed by the reference vertex Pb, and the vertexes Pc and P(C+1) selected in said first selection operation, and the vertex P(c+2) selected in said second selection operation.

7. The polygon rendering program according to claim 5 , wherein the polygon rendering program is recorded on a recording medium.