Abstract: A three-dimensional CAD/CAM system includes: a primitive generation unit using a differential polyhedron model being a set including coordinate values and normal vectors of triangle vertices, and curved line elements including start/end points being the triangle vertices and tangent vectors at the start/end points to form a curved surface by connecting sides of the differential polyhedron and form a closed surface by connecting curved surfaces with a curved surface boundary line; a storage unit storing CSG data representing a solid model in CSG representation by a tree structure of set operations of the primitives; a dexel generation unit determining an intersection point between the solid model and a straight line from the intersection point between the closed surface of the primitive and the straight line by a set operation based on the CSG data; and an NC data generation unit for positioning a tool on the basis of the dexel.

Abstract: An information processing apparatus, program, and information processing method performing validated numerics. Arithmetic operation of definite numbers a1 and b1 of the computer numbers in which real numbers A and B are defined by formulas (1) and (2) is performed to determine an absolute effective digit ? satisfying formula (3), A=a1+a2,|a1|?Cha,?Cea?a2<Cea??formula (1), B=b1+b2,|a1|?Chb,?Ceb?b2<Ceb??formula (2), (A,B)=(a,b)1+(a,b)2,?C??(a,b)2<C???formula (3). a1 and b1 are definite numbers whose numerical values are definite, and a2 and b2 are uncertain numbers whose numerical values are uncertain; C denotes a radix; ha and hb denote extended high order maxes that are minimum extended digits satisfying |a1|?Cha and |b1|?Chb, and ha and hb denote high order maxes that are integers; and ea, eb and ? denote the absolute effective digits that are integers.

Abstract: An information processing apparatus, program, and information processing method performing validated numerics. Arithmetic operation of definite numbers a1 and b1 of the computer numbers in which real numbers A and B are defined by formulas (1) and (2) is performed to determine an absolute effective digit ? satisfying formula (3), A=a1+a2, |a1|?Cha, ?Cea?a2<Cea??formula (1), B=b1+b2, |a1|?Chb, ?Ceb?b2<Ceb??formula (2), (A,B)=(a,b)1+(a,b)2, ?C??(a,b)2<C???formula (3). a1 and b1 are definite numbers whose numerical values are definite, and a2 and b2 are uncertain numbers whose numerical values are uncertain; C denotes a radix; ha and hb denote extended high order maxes that are minimum extended digits satisfying |a1|?Cha and |b1|?Chb, and ha and hb denote high order maxes that are integers; and ea, eb and ? denote the absolute effective digits that are integers.