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***********************************
* GRAPHIC OBJECTS IN GIAC/XCAS *
***********************************
=================
Short description of gen g such that g.is_symb_of_sommet(at_pnt) in C++ (or g[0]=='pnt' in Xcas)
Then g.feuille is a vecteur of length 2 or 3 :
* f=g.feuille[0] in C++ (or g[1] in Xcas) is the analytic geometric object,
* a=g.feuille[1] in C++ (or g[2] in Xcas) is the attribut for display
* g.feuille[2] in C++ (or eval(g,1)[3] in Xcas) is the name of the object, it is removed during
normal evaluation (hence the unusual syntax in Xcas to keep it)
Analytic geometric object description (the analytic object may be fetched by
f=remove_at_pnt(g) in C++ or g[1] in Xcas):
* points are coded by a complex number (in 2-d) or
by a gen of type _VECT and subtype _POINT__VECT (in 3-d)
* segments, halfline, line, geometric vectors by a gen of type _VECT and subtype listed
in dispatch.h (0 segment, _LINE__VECT, _HALFLINE__VECT, _VECTOR__VECT),
the vector has length 2 and contains the affixes of the 2 points defining it.
* polygons by a gen of type _VECT with the affixes of the vertices of the polygon
* circles (and arcs of circles) are coded by a gen of type _SYMB and sommet at_circle,
f.is_symb_of_sommet(at_circle)==true, f._SYMBptr->feuille[0] is the diameter of the circle,
f._SYMBptr->feuille[1] and [2] are the angles.
An additionnal parameter of value 1 may be used to add an angle symbol, of value
2 for an arrow inside the arc.
* function/parametric/polar plot, conics are represented with a parametrization, they are coded by a gen of type _SYMB and sommet at_curve, f.is_symb_of_sommet(at_curve)==true.
f._SYMBptr->feuille[0] is the parametrization with the affix of a point in the curve,
the variable, the discretization (min, max of parameter), and 0 or 1 (hide/show equation)
e.g. plot(sin(x),x=-5..5,xstep=0.125)[1][1]==[x+i*sin(x),x,-5,5.0625,0]
f._SYMBptr->feuille[1] is the discretization computed, ready for display (as a polygon)
Attributes description (a=g._SYMBptr->feuille[1] in C++ or g[2] in Xcas)
Attribute is either an atomic gen (an int most of the time) or a vecteur that contains the display
attribute and a curve where the geometric object may move (for point on curves). See code
below from Graph.cc (void fltk_draw) or in native/Apps/geometry.cpp (void CGeoplot::fltk_draw
and refer to dispatch_h at enum color_values for attributes values.
string the_legend;
vecteur style(get_style(a,the_legend));
int styles=style.size();
// color
int ensemble_attributs = style.front().val;
bool hidden_name = false;
if (style.front().type==_ZINT){
ensemble_attributs = mpz_get_si(*style.front()._ZINTptr);
hidden_name=true;
}
else
hidden_name=ensemble_attributs<0;
int width =(ensemble_attributs & 0x00070000) >> 16; // 3 bits
int epaisseur_point =(ensemble_attributs & 0x00380000) >> 19; // 3 bits
int type_line =(ensemble_attributs & 0x01c00000) >> 22; // 3 bits
if (type_line>4)
type_line=(type_line-4)<<8;
int type_point =(ensemble_attributs & 0x0e000000) >> 25; // 3 bits
int labelpos =(ensemble_attributs & 0x30000000) >> 28; // 2 bits
bool fill_polygon =(ensemble_attributs & 0x40000000) >> 30;
int couleur =(ensemble_attributs & 0x0000ffff);
epaisseur_point += 2;
==================
Cursors: a gen g such that g.is_symb_of_sommet(at_parameter) is a cursor, it is used to move a
1-d parameter value. There are two instructions to produce a parameter: assume and element.
* assume: may be used to define symbolic cursor, they have a numeric value that is used only when a numeric evaluation is done (or a geometric display), while the parameter will keep it's symbolic value in exact evaluation, example
assume(a=[0.4,-5,5,0.1]) returns parameter([a,-5,5,0.4,0.1]) and stores a special value in a such that
eval(a) will stay a, evalf(a) returns 0.4, (-5 and 5 are the limits, 0.1 is the step)
* element: will assign the numeric value to the parameter a in exact and numeric evaluation.
a:=element(-5..5,0.4,0.1) returns parameter([a,-5,5,0.4,0.1]) and stores 0.4 in a
(eval(a) and evalf(a) both returns 0.4)
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