Curve rendering device, curve rendering method, curve rendering program, and integrated circuit

1. A curve rendering device for rendering a curve, having a width and defined by a center line and a line width, by linear approximation of an outline of the curve, the curve rendering device comprising:

a non-transitory memory storing a program; and

a hardware processor that executes the program causing the curve rendering device to operates as:

a segmentation point calculating unit configured to calculate a plurality of segmentation points on the center line for segmenting the center line;

an offset point calculating unit configured to calculate, for each of the segmentation points, two offset points separated from the segmentation point by an equal distance on a normal to the center line at the segmentation point;

a distance calculating unit configured to calculate a distance between offset points in each of two pairs selected from four offset points calculated for two adjacent segmentation points, the offset points in each pair being located on a same side with respect to a straight line connecting the two adjacent segmentation points;

a judging unit configured to calculate a ratio between the calculated two distances using a shorter one of the distances as a denominator, and judge whether or not the ratio is greater than a predetermined value; and

a curve forming unit configured to approximate, between two partial outlines which are portions of the outline delimited at the respective normals at the two adjacent segmentation points, the longer one of the two partial outlines by using a greater number of line segments than line segments used to approximate the shorter one of the two partial outlines when the ratio is judged to be greater than the predetermined value.

2. The curve rendering device according to claim 1 , wherein

the offset point calculating unit calculates, as the two offset points separated from the segmentation point by the equal distance, points that are separated from the segmentation point by half the line width.

3. The curve rendering device according to claim 1 , wherein

the curve forming unit approximates the shorter partial outline with a single line segment, and

the segmentation point calculating unit segments the center line so that the single line segment approximating the shorter partial outline becomes equal to a predetermined length or shorter.

4. The curve rendering device according to claim 1 , wherein

the curve forming unit determines the number of line segments used to approximate the longer partial outline in relation to the ratio calculated by the judging unit.

5. The curve rendering device according to claim 4 , wherein

when approximating the longer partial outline, the curve forming unit calculates points a n and b n and vectors s n , t n , and u n , with respect to each integer from 1 to d, using following equations:

a n =a n-1 +2 n-1-d ( c n-1 −a n-1 );

b n =b n-1 +2 n-1-d ( c n-1 −b n-1 );

s n =2 -d {(2 d-(n-1) −1) u n-1 +s n-1 )};

t n =2 -d {(2 d-(n-1) −1)(− u n-1 )+ t n-1 )}; and

u n =s n +(− t n ),

where

a 0 and b 0 denote end points of the longer partial outline,

s 0 denotes a tangent vector to the center line at the point a 0 ,

t 0 denotes an inverse of a tangent vector to the center line at the point b 0 ,

c 0 denotes an intersection point of a straight line extending from the point a 0 in a direction of the vector s 0 and a straight line extending from the point b 0 in a direction of the vector t 0 , and

d denotes a division coefficient,

in the equations, a point c n denotes an intersection point of a straight line extending from the point a n in a direction of the vector s n and a straight line extending from the point b n in a direction of the vector t n , and

the curve forming unit approximates the longer partial outline with a sequence of straight lines defined by connecting (d+1) points a m (m is an integer from 0 to d), a point c d , and (d+1) points b m .

6. The curve rendering device according to claim 1 , wherein

when one of the two normals intersects with the other at a point between the offset points on the normal, the curve forming unit approximates one of the partial outlines with a plurality of curves irrespective of the judgment by the judging unit, the one of the partial outlines being located on an opposite side from the intersecting point of the normals with respect to a straight line connecting the two adjacent segmentation points.

7. A curve rendering method used in a curve rendering device for rendering a curve, having a width and defined by a center line and a line width, by linear approximation of an outline of the curve, the curve rendering device including a non-transitory memory storing a program and a hardware processor that executes the program causing the curve rendering device to operates as a segmentation point calculating unit, an offset point calculating unit, a distance calculating unit, a judging unit, and a curve forming unit, the curve rendering method comprising the steps of:

a segmentation point calculating step performed by the hardware processor configured to operate as the segmentation point calculating unit to calculate a plurality of segmentation points on the center line for segmenting the center line;

an offset point calculating step performed by the hardware processor configured to operates as the offset point calculating unit to calculate, for each of the segmentation points, two offset points separated from the segmentation point by an equal distance on a normal to the center line at the segmentation point;

a distance calculating step performed by the hardware processor configured to operate as distance calculating unit to calculate a distance between offset points in each of two pairs selected from four offset points calculated for two adjacent segmentation points, the offset points in each pair being located on a same side with respect to a straight line connecting the two adjacent segmentation points;

a judging step performed by the hardware processor configured to operate as the judging unit to calculate a ratio between the calculated two distances using athe shorter one of the distances as a denominator, and judge whether or not the ratio is greater than a predetermined value; and

a curve forming step performed by the hardware processor configured to operate as the curve forming unit to approximate, between two partial outlines which are portions of the outline delimited at the respective normals at the two adjacent segmentation points, athe longer one of the two partial outlines by using a greater number of line segments than line segments used to approximate the shorter one of the two partial outlines when the ratio is judged to be greater than the predetermined value.

8. A non-transitory computer-readable recording medium storing a curve rendering program for causing a computer to function as a curve rendering device that is for rendering a curve, having a width and defined by a center line and a line width, by linear approximation of an outline of the curve, the curve rendering program comprising code for causing the computer to function as:

a segmentation point calculating unit configured to calculate a plurality of segmentation points on the center line for segmenting the center line;

an offset point calculating unit configured to calculate, for each of the segmentation points, two offset points separated from the segmentation point by an equal distance on a normal to the center line at the segmentation point;

a distance calculating unit configured to calculate a distance between offset points in each of two pairs selected from four offset points calculated for two adjacent segmentation points, the offset points in each pair being located on a same side with respect to a straight line connecting the two adjacent segmentation points;

a judging unit configured to calculate a ratio between the calculated two distances using a shorter one of the distances as a denominator, and judge whether or not the ratio is greater than a predetermined value; and

a curve forming unit configured to approximate, between two partial outlines which are portions of the outline delimited at the respective normals at the two adjacent segmentation points, a longer one of the two partial outlines by using a greater number of line segments than line segments used to approximate the shorter one of the two partial outlines when the ratio is judged to be greater than the predetermined value.

9. An integrated circuit used in a curve rendering device for rendering a curve, having a width and defined by a center line and a line width, by linear approximation of an outline of the curve, the integrated circuit comprising:

a segmentation point calculating circuit configured to calculate a plurality of segmentation points on the center line for segmenting the center line;

an offset point calculating circuit configured to calculate, for each of the segmentation points, two offset points separated from the segmentation point by an equal distance on a normal to the center line at the segmentation point;

a distance calculating circuit configured to calculate a distance between offset points in each of two pairs selected from four offset points calculated for two adjacent segmentation points, the offset points in each pair being located on a same side with respect to a straight line connecting the two adjacent segmentation points;

a judging circuit configured to calculate a ratio between the calculated two distances using the shorter one of the distances as a denominator, and judge whether or not the ratio is greater than a predetermined value; and

a curve forming circuit configured to approximate, between two partial outlines which are portions of the outline delimited at the respective normals at the two adjacent segmentation points, a longer one of the two partial outlines by using a greater number of line segments than line segments used to approximate the shorter one of the two partial outlines when the ratio is judged to be greater than the predetermined value.