93 lines
2.8 KiB
C
93 lines
2.8 KiB
C
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/*
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Apophysis Plugin
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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*/
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typedef struct
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{
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// expo_real represents the real part of the base (a)
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double expo_real;
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// expo_imaginary represents the imaginary part of the base (b)
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double expo_imaginary;
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double expo_k;
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double expo_t;
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} Variables;
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#include "apoplugin.h"
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// Set the name of this plugin
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APO_PLUGIN("expo");
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// Define the Variables
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APO_VARIABLES(
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VAR_REAL(expo_real, -1.0),
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VAR_REAL(expo_imaginary, 1.0)
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);
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// You must call the argument "vp".
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int PluginVarPrepare(Variation* vp)
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{
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double ereal = VAR(expo_real);
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double eimag = VAR(expo_imaginary);
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VAR(expo_k) = 0.5 * log(ereal * ereal + eimag * eimag + 1e-300);
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VAR(expo_t) = atan2(eimag,ereal);
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// Always return TRUE.
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return TRUE;
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}
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// You must call the argument "vp".
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int PluginVarCalc(Variation* vp)
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{
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double expor = exp(FTx * VAR(expo_k) - FTy * VAR(expo_t));
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double snv, csv;
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fsincos(FTx * VAR(expo_t) + FTy * VAR(expo_k), &snv, &csv);
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FPx += VVAR * expor * csv;
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FPy += VVAR * expor * snv;
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return TRUE;
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}
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// Given the equation (a + ib)^z, or c^z, where c = a + ib...
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// We can rewrite it as e^(ln(c^z))...
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// Using the laws of Logs, we get e^(z * ln(c))...
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// The ln of a complex number is ln(r) + itheta, where
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// r is the radius and theta is the angle. Thus, we need
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// the radius and angle of our base number c.
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// k is what I've used to represent the radius of the number
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// c, or a + ib. t is used to represent the angle.
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// Thus, expok is the radius of c and expot is the angle.
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// Now we have e^(z * (ln(k) + it)), or e^((x + iy) * (ln(k) + it))
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// Simplifying this down, we get...
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// e^(xln(k) - yt) * e^i(xt + yln(k))
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// Because a Complex Number can be presented as
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// r * e^itheta, where r is the radius and theta is the angle,
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// We can say that r' = e^(xln(k) - yt)
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// And that theta' = xt + yln(k)
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// For optimization (as recommended by Joel) we calculate k,
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// the radius of our complex number, as the ln of k,
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// because we never need k to be on its own (it is always
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// logged before it is used).
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// That's the equation!
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