Apparatus and method for generating progressive polygon data, and apparatus and method for generating three-dimensional real-time graphics using the same

A 3D real-time graphics generator, comprising:

• a rendering polygon number determinator for determining a number of polygons for rendering 3D polygon data;
• a 3D polygon data producer for producing 3D polygon data based on progressive polygon data in accordance with the number of polygons determined by the rendering polygon number determinator;
• a progressive polygon data generator generating the progressive polygon data, comprising:
• a basic vertex determinator determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determinator determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculator progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex determinator in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex determinator;
• a detailed polygon data generator generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex determinator, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing part combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• an outputting unit outputting the generated progressive polygon data,
• wherein said basic vertex determinator determines vertices of the basic polyhedron by selection of an operator,
• wherein said detailed vertex determinator comprises:
• an approximation level calculator calculating a difference between an area of each face of the basic polyhedron and an area on a surface of the 3D object defined by line segments connecting vertices of each face of the basic polyhedron;
• a comparator comparing the difference calculated by the approximation level calculator with a predetermined value;
• and
• a progressive vertex determinator determining a new vertex closer to the surface of the 3D object than a corresponding face when the comparator determines that the difference is the predetermined value or more, and not determining a new vertex when the difference is determined to be smaller than the predetermined value,
• wherein when a new vertex is determined by said progressive vertex determinator, the approximation level calculator calculates a difference in area with respect to a polyhedron defined by the corresponding face and the new vertex, and the progressive vertex determinator determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex determinator no longer determines a new vertex.

A method for generating 3D real-time graphics, comprising:

• a rendering polygon number determining operation determining the number of polygons for rendering 3D polygon data;
• and
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined by the rendering polygon number determining operation;
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex operation determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex operation, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• an outputting operation outputting the progressively generated polygon data,
• wherein said basic vertex operation determines vertices of the basic polyhedron by selection of an operator,
• wherein said detailed vertex operation comprises:
• an approximation level operation calculating a difference between an area of each face of the basic polyhedron and an area on a surface of the 3D object defined by line segments connecting vertices of each face of the basic polyhedron;
• a comparator operation comparing the difference calculated by the approximation level operation with a predetermined value;
• and
• a progressive vertex operation determining a new vertex closer to the surface of the 3D object than a corresponding face when the comparator operation determines that the difference is the predetermined value or more, and not determining a new vertex when the difference is determined to be smaller than the predetermined value,
• wherein when a new vertex is determined by said progressive vertex operation, the approximation level operation calculates a difference in area with respect to a polyhedron defined by the corresponding face and the new vertex, and the progressive vertex operation determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex operation no longer determines a new vertex.

A computer-readable recording medium storing a program executing a process comprising:

• a rendering polygon number determining operation determining the number of polygons for rendering 3D polygon data;
• a 3D polygon data producing operation producing 3D polygon data based on the progressive polygon data, based on the number of polygons determined in the rendering polygon number determining operation,
• wherein in the 3D polygon data producing operation, the 3D polygon data is produced by determining vertices constituting the 3D polygon data for rendering an object, based on the number of polygons determined in the rendering polygon number determining operation,
• using a progressive polygon data generator to generate the progressive polygon data, by performing:
• a basic vertex operation determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex operation determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex operation, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object,
• wherein, said basic vertex determinator determines vertices of the basic polyhedron by selection of an operator,
• wherein said detailed vertex operation comprises:
• an approximation level operation calculating a difference between an area of each face of the basic polyhedron and an area on a surface of the 3D object defined by line segments connecting vertices of each face of the basic polyhedron;
• a comparator operation comparing the difference calculated by the approximation level operation with a predetermined value;
• a progressive vertex operation determining a new vertex closer to the surface of the 3D object than a corresponding face when the comparator operation determines that the difference is the predetermined value or more, and not determining a new vertex when the difference is determined to be smaller than the predetermined value;
• and
• an outputting operation outputting the generated progressive polygon data,
• wherein when a new vertex is determined by said progressive vertex operation, the approximation level operation calculates a difference in area with respect to a polyhedron defined by the corresponding face and the new vertex, and the progressive vertex operation determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex operation no longer determines a new vertex.

A 3D real-time graphics generator comprising:

• a rendering polygon number determinator for determining the number of polygons for rendering 3D polygon data;
• and
• a 3D polygon data producer for producing 3D polygon data based on progressive polygon data generated by the progressive polygon data generator in accordance with the number of polygons determined by the rendering polygon number determinator,
• wherein the progressive polygon data is generated by a progressive polygon generator comprising:
• a basic vertex determinator determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determinator determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculator progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex determinator in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex determinator;
• a detailed polygon data generator generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex determinator, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing part combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• and
• an outputting unit outputting the generated progressive polygon data.

A method for generating 3D real-time graphics comprising;

• a rendering polygon number determining operation determining the number of polygons for rendering 3D polygon data;
• and
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined by the rendering polygon number determining operation;
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex operation determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex operation, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data.

A computer-readable recording medium storing a program executing a process comprising:

• a rendering polygon number determining operation determining the number of polygons for rendering 3D polygon data;
• and
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined in the rendering polygon number determining operation,
• wherein in the 3D polygon data producing operation, the 3D polygon data is produced by determining vertices constituting the 3D polygon data for rendering an object, based on the number of polygons determined in the rendering polygon number determining operation;
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex operation determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex operation, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data.

A progressive polygon data generator, comprising:

• a basic vertex determinator for determining vertices of polygons approximate to an outer edge shape of cross-sections virtually segmenting a 3D object such that the determined vertices are vertices of a basic polyhedron approximate to a shape of the 3D object;
• a detailed vertex determinator for progressively determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron based on the level of approximation;
• a detailed vertex coordinate calculator for progressively calculating relative position coordinates of the detailed polyhedron vertices determined by said detailed vertex determinator in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator for generating basic polygon data for representing the basic polyhedron based on information on the vertices of the basic polyhedron determined by the basic vertex determinator;
• a detailed polygon data generator for generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of the detailed polyhedron determined by the detailed vertex determinator, which information is described in relative position coordinates in a relative coordinate system;
• and
• a polygon progressing part for combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering respective models in each progressive level in a corresponding level of approximation to the 3D object.

A 3D real-time graphics generator comprising:

• a rendering polygon number determinator determining the number of polygons for rendering 3D polygon data;
• a 3D polygon data producer for producing 3D polygon data based on progressive polygon data in accordance with the number of polygons determined by the rendering polygon number determinator,
• wherein the progressive polygon data is generated by a progressive polygon data generator, comprising:
• a basic vertex determinator determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determinator determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculator progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex determinator in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex determinator;
• a detailed polygon data generator generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex determinator, which information is described in relative position coordinates in the relative coordinate system;
• a polygon progressing part combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• an outputting unit outputting the generated progressive polygon data,
• wherein the 3D object is a 3D object represented by the original polygon data obtained by geometric modeling of the 3D object,
• the polygon approximate to an outer edge shape of each cross-section determined by the basic vertex determinator is a quadrilateral which is defined by control points at which line segments intersect a face virtually bisecting the 3D object so as to form a second polygonal shape by connecting the control points and the polygon approximate to each cross-section which is a quadrilateral defined by four vertices that divide a total length of sides of the second polygonal shape into four equal lengths,
• wherein the detailed vertex determinator comprises:
• an approximation level calculator calculating a difference between a length of each side of the quadrilateral and a total length of sides of the second polygonal shape between both ends of each side of the quadrilateral;
• a comparator comparing the difference calculated by the approximation level calculator with a predetermined value;
• and
• a progressive vertex determinator determining a point that divides into two equal lengths the total length of the sides of the second polygonal shape between both ends of the side of the quadrilateral as a vertex of a polygon in a higher level of approximation when the comparator determines that the difference is the predetermined value or more, and not determining a vertex of a polygon in a higher level of approximation when the difference is determined to be smaller than the predetermined value,
• when a vertex of a polygon in a higher level of approximation is determined by the progressive vertex determinator, the approximation level calculator calculates the difference with respect to a newly produced side of the polygon whose vertex is determined, and the progressive vertex determinator determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex determinator no longer determines a vertex of a polygon in a higher level of approximation.

A method for generating 3D real-time graphics using progressive polygon data, comprising:

• a rendering polygon number determining operation determining a number of polygons for rendering 3D polygon data;
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined by the rendering polygon number determining operation,
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of polygons approximate to an outer edge shape of cross-sections virtually segmenting a 3D object such that the determined vertices are vertices of a basic polyhedron approximate to a shape of the 3D object;
• a detailed vertex operation progressively determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the detailed polyhedron vertices determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator operation generating basic polygon data for representing the basic polyhedron based on information on the vertices of the basic polyhedron determined by the basic vertex operation;
• a detailed polygon data generator operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of the detailed polyhedron determined by the detailed vertex operation, which information is described in relative position coordinates in a relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering respective models in each progressive level in a corresponding level of approximation to the 3D object;
• an outputting operation outputting the generated progressive polygon data,
• wherein the 3D object is a 3D object represented by the original polygon data obtained by geometric modeling of the 3D object,
• the polygon approximate to an outer edge shape of each cross-section determined by the basic vertex determinator is a quadrilateral which is defined by control points at which line segments intersect a face virtually bisecting the 3D object so as to form a second polygonal shape by connecting the control points and the polygon approximate to each cross-section which is a quadrilateral defined by four vertices that divide a total length of sides of the second polygonal shape into four equal lengths,
• wherein the detailed vertex operation comprises:
• an approximation level operation calculating a difference between a length of each side of the quadrilateral and a total length of sides of the second polygonal shape between both ends of each side of the quadrilateral;
• a comparator operation comparing the difference calculated by the approximation level calculator with a predetermined value;
• and
• a progressive vertex operation determining a point that divides into two equal lengths the total length of the sides of the second polygonal shape between both ends of the side of the quadrilateral as a vertex of a polygon in a higher level of approximation when the comparator operation determines that the difference is the predetermined value or more, and not determining a vertex of a polygon in a higher level of approximation when the difference is determined to be smaller than the predetermined value,
• when a vertex of a polygon in a higher level of approximation is determined by the progressive vertex operation, the approximation level calculator calculates the difference with respect to a newly produced side of the polygon whose vertex is determined, and the progressive vertex operation determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex operation no longer determines a vertex of a polygon in a higher level of approximation.

A computer-readable recording medium storing a program executing a process comprising:

• a rendering polygon number determining operation determining a number of polygons for rendering 3D polygon data;
• a 3D polygon data producing operation producing 3D polygon data based on the progressive polygon data, based on the number of polygons determined in the rendering polygon number determining operation,
• wherein in the 3D polygon data producing operation, the 3D polygon data is produced by determining vertices constituting the 3D polygon data for rendering an object, based on the number of polygons determined in the rendering polygon number determining operation;
• using a progressive polygon data generator to generator the progressive polygon data by performing:
• a basic vertex operation determining vertices of polygons approximate to an outer edge shape of cross-sections virtually segmenting a 3D object such that the determined vertices are vertices of a basic polyhedron approximate to a shape of the 3D object;
• a detailed vertex operation progressively determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron based on the level of approximation;
• a detailed vertex coordinate operation progressively calculating relative position coordinates of the detailed polyhedron vertices determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator operation generating basic polygon data for representing the basic polyhedron based on information on the vertices of the basic polyhedron determined by the basic vertex operation;
• a detailed polygon data generator operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of the detailed polyhedron determined by the detailed vertex operation, which information is described in relative position coordinates in a relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering respective models in each progressive level in a corresponding level of approximation to the 3D object;
• an outputting operation outputting the generated progressive polygon data,
• wherein the 3D object is a 3D object represented by the original polygon data obtained by geometric modeling of the 3D object,
• the polygon approximate to an outer edge shape of each cross-section determined by the basic vertex determinator is a quadrilateral which is defined by control points at which line segments intersect a face virtually bisecting the 3D object so as to form a second polygonal shape by connecting the control points and the polygon approximate to each cross-section which is a quadrilateral defined by four vertices that divide a total length of sides of the second polygonal shape into four equal lengths,
• wherein the detailed vertex operation comprises:
• an approximation level operation calculating a difference between a length of each side of the quadrilateral and a total length of sides of the second polygonal shape between both ends of each side of the quadrilateral;
• a comparator operation comparing the difference calculated by the approximation level calculator with a predetermined value;
• and
• a progressive vertex operation determining a point that divides into two equal lengths the total length of the sides of the second polygonal shape between both ends of the side of the quadrilateral as a vertex of a polygon in a higher level of approximation when the comparator operation determines that the difference is the predetermined value or more, and not determining a vertex of a polygon in a higher level of approximation when the difference is determined to be smaller than the predetermined value,
• when a vertex of a polygon in a higher level of approximation is determined by the progressive vertex operation, the approximation level calculator calculates the difference with respect to a newly produced side of the polygon whose vertex is determined, and the progressive vertex operation determines a vertex of a polygon in a higher level of approximation recursively, until the progressive vertex operation no longer determines a vertex of a polygon in a higher level of approximation.

A 3D real-time graphics generator comprising:

• a rendering polygon number determinator determining the number of polygons for rendering 3D polygon data;
• a 3D polygon data producer producing 3D polygon data based on the progressive polygon data in accordance with the number of polygons determined by the rendering polygon number determinator,
• wherein the progressive polygon data is generated by a progressive polygon data generator comprising:
• a basic vertex determinator determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determinator determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the approximation of the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculator progressively calculating relative position coordinates of the vertices of the detailed polyhedron determined by said detailed vertex determinator in a relative coordinate system based on a plurality of predetermined vertices in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data generator generating basic polygon data representing the basic polyhedron based on the vertices of the basic polyhedron determined by said basic vertex determinator;
• a detailed polygon data generator generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the vertices of each detailed polyhedron determined by said detailed vertex determinator, which information is described in relative position coordinates in the relative coordinate system;
• and
• a polygon progressing part combining the basic polygon data and the detailed polygon data and progressively generating polygon data for rendering respective models in each progressive level in corresponding levels of approximation to the 3D object;
• and
• an outputting unit outputting the generated progressive polygon data.

A method for generating 3D real-time graphics comprising:

• a rendering polygon number determining operation determining a number of polygons for rendering 3D polygon data;
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined a by the rendering polygon number determining operation;
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of polygons approximate to an outer edge shape of cross-sections virtually segmenting a 3D object such that the determined vertices are vertices of a basic polyhedron approximate to a shape of the 3D object;
• a detailed vertex operation progressively determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron based on the level of approximation;
• a detailed vertex coordinate operation for progressively calculating relative position coordinates of the detailed polyhedron vertices determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data for representing the basic polyhedron based on information on the vertices of the basic polyhedron determined by the basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of the detailed polyhedron determined by the detailed vertex operation, which information is described in relative position coordinates in a relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering respective models in each progressive level in a corresponding level of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data.

A computer-readable recording medium storing a program executing a process comprising:

• a rendering polygon number determining operation determining a number of polygons for rendering 3D polygon data;
• a 3D polygon data producing operation producing 3D polygon data based on progressive polygon data, based on the number of polygons determined in the rendering polygon number determining operation,
• wherein in the 3D polygon data producing operation, the 3D polygon data is produced by determining vertices constituting the 3D polygon data for rendering an object, based on the number of polygons determined in the rendering polygon number determining operation;
• using a progressive polygon data generator to generate the progressive polygon data by performing:
• a basic vertex operation determining vertices of polygons approximate to an outer edge shape of cross-sections virtually segmenting a 3D object such that the determined vertices are vertices of a basic polyhedron approximate to a shape of the 3D object;
• a detailed vertex operation progressively determining vertices of a detailed polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron based on the level of approximation;
• a detailed vertex coordinate operation for progressively calculating relative position coordinates of the detailed polyhedron vertices determined by said detailed vertex operation in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the detailed polyhedron;
• a basic polygon data operation generating basic polygon data for representing the basic polyhedron based on information on the vertices of the basic polyhedron determined by the basic vertex operation;
• a detailed polygon data operation generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of the detailed polyhedron determined by the detailed vertex operation, which information is described in relative position coordinates in a relative coordinate system;
• a polygon progressing operation combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering respective models in each progressive level in a corresponding level of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data.

A method for generating progressive polygon data comprising:

• a basic vertex determining operation of determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determining operation of determining vertices of a polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculating operation of calculating relative position coordinates of vertices of a progressively determined polyhedron in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the polyhedron,
• a basic polygon data generating operation of generating basic polygon data for representing basic polyhedron based on the information on vertices of a basic polyhedron determined by the basic vertex determining operation;
• a detailed polygon data generating operation of generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of detailed polyhedron determined by the detailed vertex determining operation, which information is described in relative position coordinates in a relative coordinate system;
• and
• a polygon progressing operation of combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering model in each progressive level in a corresponding level of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data,
• wherein the detailed vertex determining operation and the detailed vertex coordinate calculating operation are performed until the level of approximation reaches a predetermined level of approximation.

A computer-readable recording medium storing a program, the program comprising:

• a basic vertex determining operation of determining vertices of a basic polyhedron approximate to a shape of a 3D object;
• a detailed vertex determining operation of determining vertices of a polyhedron in a level of approximation to the 3D object that is higher than the basic polyhedron progressively based on the level of approximation;
• a detailed vertex coordinate calculating operation of calculating relative position coordinates of vertices of a progressively determined polyhedron in a relative coordinate system based on a plurality of predetermined vertices of a polyhedron in a level of approximation that is lower than the polyhedron,
• a basic polygon data generating operation of generating basic polygon data for representing basic polyhedron based on the information on vertices of a basic polyhedron determined by the basic vertex determining operation;
• a detailed polygon data generating operation of generating detailed polygon data for representing each progressive detailed polyhedron in a corresponding level of approximation to the 3D object based on the information on vertices of detailed polyhedron determined by the detailed vertex determining operation, which information is described in relative position coordinates in a relative coordinate system;
• a polygon progressing operation of combining the basic polygon data and the detailed polygon data and generating progressive polygon data for rendering model in each progressive level in a corresponding level of approximation to the 3D object;
• and
• an outputting operation outputting the generated progressive polygon data,
• wherein the detailed vertex determining operation and the detailed vertex coordinate calculating operation are performed until the level of approximation reaches a predetermined level of approximation.

A computer-readable recording medium storing progressive polygon data,

• wherein 3D polygon data representing an 3D object is produced based on the progressive polygon in accordance with a determined number of polygons;
• the progressive polygon data comprises information about vertices of a basic polyhedron approximate to a shape of the 3D object and information about a plurality of detailed vertices obtained by sequentially computing vertices from the vertices of the basic polyhedron in accordance with the determined number of polygons so that a polyhedron in a higher level of approximation to the 3D object is generated;
• the information of the detailed vertices is represented in the form of relative position coordinates in a relative coordinate system determined based on a plurality of predetermined vertices of a polyhedron not including the detailed vertices;
• and
• the progressive polygon data is outputted.