3.2.2 Curved coordinates

Method on mglGraph (C++, Python): void SetFunc (const char *EqX, const char *EqY, const char *EqZ="", const char *EqA="")

C function: void mgl_set_func (HMGL gr, const char *EqX, const char *EqY, const char *EqZ)

C function: void mgl_set_func_ext (HMGL gr, const char *EqX, const char *EqY, const char *EqZ, const char *EqA)

Sets transformation formulas for curvilinear coordinate. Each string should contain mathematical expression for real coordinate depending on internal coordinates ‘x’, ‘y’, ‘z’ and ‘a’ or ‘c’ for colorbar. For example, the cylindrical coordinates are introduced as Axis("x*cos(y)", "x*sin(y)", "z");. For removing of formulas the corresponding parameter should be empty or NULL. Using transformation formulas will slightly slowing the program. Parameter EqA set the similar transformation formula for color scheme. See section Textual formulas.

Method on mglGraph (C++, Python): void SetCoor (int how)

C function: void mgl_set_coor (HMGL gr, int how)

Sets one of the predefined transformation formulas for curvilinear coordinate. Paramater how define the coordinates: mglCartesian=0 – Cartesian coordinates (no transformation); mglPolar=1 – Polar coordiantes x_n=x*cos(y),y_n=x*sin(y), z_n=z; mglSpherical=2 – Sperical coordinates x_n=x*sin(y)*cos(z), y_n=x*sin(y)*sin(z), z_n=x*cos(y); mglParabolic=3 – Parabolic coordinates x_n=x*y, y_n=(x*x-y*y)/2, z_n=z; mglParaboloidal=4 – Paraboloidal coordinates x_n=(x*x-y*y)*cos(z)/2, y_n=(x*x-y*y)*sin(z)/2, z_n=x*y; mglOblate=5 – Oblate coordinates x_n=cosh(x)*cos(y)*cos(z), y_n=cosh(x)*cos(y)*sin(z), z_n=sinh(x)*sin(y); mglProlate=6 – Prolate coordinates x_n=sinh(x)*sin(y)*cos(z), y_n=sinh(x)*sin(y)*sin(z), z_n=cosh(x)*cos(y); mglElliptic=7 – Elliptic coordinates x_n=cosh(x)*cos(y), y_n=sinh(x)*sin(y), z_n=z; mglToroidal=8 – Toroidal coordinates x_n=sinh(x)*cos(z)/(cosh(x)-cos(y)), y_n=sinh(x)*sin(z)/(cosh(x)-cos(y)), z_n=sin(y)/(cosh(x)-cos(y)); mglBispherical=9 – Bispherical coordinates x_n=sin(y)*cos(z)/(cosh(x)-cos(y)), y_n=sin(y)*sin(z)/(cosh(x)-cos(y)), z_n=sinh(x)/(cosh(x)-cos(y)); mglBipolar=10 – Bipolar coordinates x_n=sinh(x)/(cosh(x)-cos(y)), y_n=sin(y)/(cosh(x)-cos(y)), z_n=z.

Method on mglGraph (C++, Python): void Ternary (bool tern)

C function: void mgl_set_ternary (HMGL gr, int tern)

The function sets to draws Ternary plot. This special plot is for 3 dependent coordinates (components) a, b, c so that a+b+c=1. MathGL uses only 2 independent coordinates a=x and b=y since it is enough to plot everything. At this third coordinate z act as another parameter to produce contour lines, surfaces and so on. See section Ternary plot sample, for sample code and picture.