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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 orNULL
. 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 or Quaternary plot. 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. Use
Ternary(0)
for returning to usual axis. See section Ternary axis, for sample code and picture.
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