Application module: B spline geometry ISO/TS 10303-1801:2011-02(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviated terms
    3.1 Terms and definitions
    3.2 Abbreviated terms

4 Information requirements
   4.1 Required AM ARM
   4.2 ARM type definitions
   4.3 ARM entity definitions
   4.4 ARM function definitions
5 Module interpreted model
   5.1 Mapping specification
   5.2 MIM EXPRESS short listing

A MIM short names
B Information object registration
C ARM EXPRESS-G   EXPRESS-G
D MIM EXPRESS-G   EXPRESS-G
E Computer interpretable listings
Bibliography
Index

(*
ISO TC184/SC4/WG12 N7190 - ISO/TS 10303-1801 B spline geometry - EXPRESS ARM
Supersedes ISO TC184/SC4/WG12 N6875
*)


SCHEMA B_spline_geometry_arm;

 USE FROM Basic_geometry_arm;    -- ISO/TS 10303-1652


TYPE knot_specification = ENUMERATION OF
   (bezier,
    quasi_uniform,
    uniform);
END_TYPE;

TYPE parameter_value = REAL;
END_TYPE;

ENTITY B_spline_curve
  ABSTRACT SUPERTYPE OF (ONEOF (Curve_with_explicit_knots,
                                Curve_with_implicit_knots)
                        ANDOR Rational_b_spline_curve)
  SUBTYPE OF (Bounded_curve);
  degree : INTEGER;
  control_points : LIST[2:?] OF Cartesian_point;
  closed : LOGICAL;
WHERE
  WR1: ('B_SPLINE_GEOMETRY_ARM.CURVE_WITH_EXPLICIT_KNOTS' IN TYPEOF(self)) OR ('B_SPLINE_GEOMETRY_ARM.CURVE_WITH_IMPLICIT_KNOTS' IN TYPEOF(self));
END_ENTITY;

ENTITY B_spline_surface
  ABSTRACT SUPERTYPE OF (ONEOF (Surface_with_explicit_knots,
                                Surface_with_implicit_knots)
                        ANDOR Rational_b_spline_surface)
  SUBTYPE OF (Bounded_surface);
  u_degree : INTEGER;
  v_degree : INTEGER;
  control_points : LIST[2:?] OF LIST[2:?] OF Cartesian_point;
  u_closed : LOGICAL;
  v_closed : LOGICAL;
WHERE
  WR1: ('B_SPLINE_GEOMETRY_ARM.SURFACE_WITH_EXPLICIT_KNOTS' IN TYPEOF(self)) OR ('B_SPLINE_GEOMETRY_ARM.SURFACE_WITH_IMPLICIT_KNOTS' IN TYPEOF(self));
END_ENTITY;

ENTITY Curve_with_explicit_knots
  SUBTYPE OF (B_spline_curve);
  knot_multiplicities : LIST[2:?] OF INTEGER;
  knot_values : LIST[2:?] OF parameter_value;
WHERE
  WR1: SIZEOF(knot_multiplicities) = SIZEOF(knot_values);
END_ENTITY;

ENTITY Curve_with_implicit_knots
  SUBTYPE OF (B_spline_curve);
  knot_type : knot_specification;
END_ENTITY;

ENTITY Rational_b_spline_curve
  SUBTYPE OF (B_spline_curve);
  weight_values : LIST[2:?] OF REAL;
WHERE
  WR1: SIZEOF(weight_values) = SIZEOF(SELF\B_spline_curve.control_points);
  WR2: positive_curve_weights(SELF);
END_ENTITY;

ENTITY Rational_b_spline_surface
  SUBTYPE OF (B_spline_surface);
  weight_values : LIST[2:?] OF LIST[2:?] OF REAL;
WHERE
  WR1: (SIZEOF(weight_values) = SIZEOF(SELF\B_spline_surface.control_points)) AND (SIZEOF(weight_values[1]) = SIZEOF(SELF\B_spline_surface.control_points[1]));
  WR2: positive_surface_weights(SELF);
END_ENTITY;

ENTITY Surface_with_explicit_knots
  SUBTYPE OF (B_spline_surface);
  u_knot_multiplicities : LIST[2:?] OF INTEGER;
  u_knot_values : LIST[2:?] OF parameter_value;
  v_knot_multiplicities : LIST[2:?] OF INTEGER;
  v_knot_values : LIST[2:?] OF parameter_value;
WHERE
  WR1: SIZEOF(u_knot_multiplicities) = SIZEOF(u_knot_values);
  WR2: SIZEOF(v_knot_multiplicities) = SIZEOF(v_knot_values);
END_ENTITY;

ENTITY Surface_with_implicit_knots
  SUBTYPE OF (B_spline_surface);
  knot_type : knot_specification;
END_ENTITY;

FUNCTION positive_curve_weights
 (bsc : Rational_b_spline_curve) : BOOLEAN; 
LOCAL
     result : BOOLEAN := TRUE;
   END_LOCAL;

   REPEAT i := 1 TO SIZEOF(bsc.weight_values);
     IF bsc.weight_values[i] <= 0.0  THEN
       result := FALSE;
       RETURN(result);
     END_IF;
   END_REPEAT;
   RETURN(result);
END_FUNCTION;

FUNCTION positive_surface_weights
 (bss : Rational_b_spline_surface) : BOOLEAN; 
LOCAL
     result        : BOOLEAN := TRUE;
   END_LOCAL;
   
   REPEAT i := 1 TO SIZEOF(bss.weight_values);
     REPEAT j := 0 TO SIZEOF(bss.weight_values[1]);
       IF (bss.weight_values[i][j] <= 0.0)  THEN
         result := FALSE;
         RETURN(result);
       END_IF;
     END_REPEAT;
   END_REPEAT;
   RETURN(result);
END_FUNCTION;

END_SCHEMA;  -- B_spline_geometry_arm


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