4.3.2 Curved coordinates

MGL command: axis 'fx' 'fy' 'fz' ['fa'='']

Method on mglGraph: 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, 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 SetFunc("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.

MGL command: axis how

Method on mglGraph: 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 coordinates 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; mglLogLog=11 – log-log coordinates x_n=lg(x), y_n=lg(y), z_n=lg(z); mglLogX=12 – log-x coordinates x_n=lg(x), y_n=y, z_n=z; mglLogY=13 – log-y coordinates x_n=x, y_n=lg(y), z_n=z.

MGL command: ternary val

Method on mglGraph: void Ternary (int tern)

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

The function sets to draws Ternary (tern=1), Quaternary (tern=2) plot or projections (tern=4,5,6).

Ternary plot is special plot 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.

Correspondingly, Quaternary plot is plot for 4 dependent coordinates a, b, c and d so that a+b+c+d=1. MathGL uses only 3 independent coordinates a=x, b=y and d=z since it is enough to plot everything.

Projections can be obtained by adding value 4 to tern argument. So, that tern=4 will draw projections in Cartesian coordinates, tern=5 will draw projections in Ternary coordinates, tern=6 will draw projections in Quaternary coordinates.

Use Ternary(0) for returning to usual axis. See section Ternary axis, for sample code and picture. See section Axis projection, for sample code and picture.

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