mirror of
https://github.com/brl/mutter.git
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d2058255b3
Never used in mutter AFAICT. Part-of: <https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/3178>
305 lines
8.4 KiB
C
305 lines
8.4 KiB
C
/*
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* Clutter.
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*
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* An OpenGL based 'interactive canvas' library.
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*
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* Authored By Tomas Frydrych <tf@openedhand.com>
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*
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* Copyright (C) 2007 OpenedHand
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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*
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* This library 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 GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "clutter/clutter-build-config.h"
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#include <glib.h>
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#include <string.h>
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#include "clutter/clutter-bezier.h"
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#include "clutter/clutter-debug.h"
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/****************************************************************************
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* ClutterBezier -- representation of a cubic bezier curve *
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* (private; a building block for the public bspline object) *
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****************************************************************************/
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/*
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* The t parameter of the bezier is from interval <0,1>, so we can use
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* 14.18 format and special multiplication functions that preserve
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* more of the least significant bits but would overflow if the value
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* is > 1
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*/
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#define CBZ_T_Q 18
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#define CBZ_T_ONE (1 << CBZ_T_Q)
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#define CBZ_T_MUL(x,y) ((((x) >> 3) * ((y) >> 3)) >> 12)
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#define CBZ_T_POW2(x) CBZ_T_MUL (x, x)
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#define CBZ_T_POW3(x) CBZ_T_MUL (CBZ_T_POW2 (x), x)
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#define CBZ_T_DIV(x,y) ((((x) << 9)/(y)) << 9)
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/*
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* Constants for sampling of the bezier
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*/
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#define CBZ_T_SAMPLES 128
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#define CBZ_T_STEP (CBZ_T_ONE / CBZ_T_SAMPLES)
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#define CBZ_L_STEP (CBZ_T_ONE / CBZ_T_SAMPLES)
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#define FIXED_BITS (32)
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#define FIXED_Q (FIXED_BITS - 16)
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#define FIXED_FROM_INT(x) ((x) << FIXED_Q)
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typedef gint32 _FixedT;
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/*
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* This is a private type representing a single cubic bezier
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*/
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struct _ClutterBezier
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{
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/*
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* bezier coefficients -- these are calculated using multiplication and
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* addition from integer input, so these are also integers
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*/
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gint ax;
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gint bx;
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gint cx;
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gint dx;
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gint ay;
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gint by;
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gint cy;
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gint dy;
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/* length of the bezier */
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guint length;
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};
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ClutterBezier *
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_clutter_bezier_new (void)
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{
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return g_new0 (ClutterBezier, 1);
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}
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void
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_clutter_bezier_free (ClutterBezier * b)
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{
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if (G_LIKELY (b))
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{
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g_free (b);
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}
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}
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static gint
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_clutter_bezier_t2x (const ClutterBezier * b, _FixedT t)
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{
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/*
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* NB -- the int coefficients can be at most 8192 for the multiplication
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* to work in this fashion due to the limits of the 14.18 fixed.
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*/
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return ((b->ax*CBZ_T_POW3(t) + b->bx*CBZ_T_POW2(t) + b->cx*t) >> CBZ_T_Q)
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+ b->dx;
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}
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static gint
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_clutter_bezier_t2y (const ClutterBezier * b, _FixedT t)
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{
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/*
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* NB -- the int coefficients can be at most 8192 for the multiplication
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* to work in this fashion due to the limits of the 14.18 fixed.
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*/
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return ((b->ay*CBZ_T_POW3(t) + b->by*CBZ_T_POW2(t) + b->cy*t) >> CBZ_T_Q)
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+ b->dy;
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}
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/*
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* Advances along the bezier to relative length L and returns the coordinances
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* in knot
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*/
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void
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_clutter_bezier_advance (const ClutterBezier *b, gint L, ClutterKnot * knot)
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{
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_FixedT t = L;
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knot->x = _clutter_bezier_t2x (b, t);
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knot->y = _clutter_bezier_t2y (b, t);
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CLUTTER_NOTE (MISC, "advancing to relative pt %f: t %f, {%d,%d}",
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(double) L / (double) CBZ_T_ONE,
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(double) t / (double) CBZ_T_ONE,
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knot->x, knot->y);
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}
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static int
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sqrti (int number)
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{
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#if defined __SSE2__
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/* The GCC built-in with SSE2 (sqrtsd) is up to twice as fast as
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* the pure integer code below. It is also more accurate.
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*/
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return __builtin_sqrt (number);
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#else
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/* This is a fixed point implementation of the Quake III sqrt algorithm,
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* described, for example, at
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* http://www.codemaestro.com/reviews/review00000105.html
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*
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* While the original QIII is extremely fast, the use of floating division
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* and multiplication makes it perform very on arm processors without FPU.
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*
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* The key to successfully replacing the floating point operations with
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* fixed point is in the choice of the fixed point format. The QIII
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* algorithm does not calculate the square root, but its reciprocal ('y'
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* below), which is only at the end turned to the inverse value. In order
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* for the algorithm to produce satisfactory results, the reciprocal value
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* must be represented with sufficient precision; the 16.16 we use
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* elsewhere in clutter is not good enough, and 10.22 is used instead.
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*/
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_FixedT x;
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uint32_t y_1; /* 10.22 fixed point */
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uint32_t f = 0x600000; /* '1.5' as 10.22 fixed */
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union
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{
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float f;
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uint32_t i;
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} flt, flt2;
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flt.f = number;
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x = FIXED_FROM_INT (number) / 2;
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/* The QIII initial estimate */
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flt.i = 0x5f3759df - ( flt.i >> 1 );
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/* Now, we convert the float to 10.22 fixed. We exploit the mechanism
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* described at http://www.d6.com/users/checker/pdfs/gdmfp.pdf.
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*
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* We want 22 bit fraction; a single precision float uses 23 bit
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* mantisa, so we only need to add 2^(23-22) (no need for the 1.5
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* multiplier as we are only dealing with positive numbers).
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*
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* Note: we have to use two separate variables here -- for some reason,
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* if we try to use just the flt variable, gcc on ARM optimises the whole
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* addition out, and it all goes pear shape, since without it, the bits
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* in the float will not be correctly aligned.
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*/
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flt2.f = flt.f + 2.0;
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flt2.i &= 0x7FFFFF;
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/* Now we correct the estimate */
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y_1 = (flt2.i >> 11) * (flt2.i >> 11);
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y_1 = (y_1 >> 8) * (x >> 8);
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y_1 = f - y_1;
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flt2.i = (flt2.i >> 11) * (y_1 >> 11);
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/* If the original argument is less than 342, we do another
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* iteration to improve precision (for arguments >= 342, the single
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* iteration produces generally better results).
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*/
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if (x < 171)
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{
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y_1 = (flt2.i >> 11) * (flt2.i >> 11);
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y_1 = (y_1 >> 8) * (x >> 8);
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y_1 = f - y_1;
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flt2.i = (flt2.i >> 11) * (y_1 >> 11);
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}
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/* Invert, round and convert from 10.22 to an integer
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* 0x1e3c68 is a magical rounding constant that produces slightly
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* better results than 0x200000.
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*/
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return (number * flt2.i + 0x1e3c68) >> 22;
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#endif
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}
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void
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_clutter_bezier_init (ClutterBezier *b,
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gint x_0, gint y_0,
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gint x_1, gint y_1,
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gint x_2, gint y_2,
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gint x_3, gint y_3)
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{
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_FixedT t;
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int i;
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int xp = x_0;
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int yp = y_0;
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_FixedT length [CBZ_T_SAMPLES + 1];
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#if 0
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g_debug ("Initializing bezier at {{%d,%d},{%d,%d},{%d,%d},{%d,%d}}",
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x0, y0, x1, y1, x2, y2, x3, y3);
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#endif
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b->dx = x_0;
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b->dy = y_0;
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b->cx = 3 * (x_1 - x_0);
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b->cy = 3 * (y_1 - y_0);
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b->bx = 3 * (x_2 - x_1) - b->cx;
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b->by = 3 * (y_2 - y_1) - b->cy;
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b->ax = x_3 - 3 * x_2 + 3 * x_1 - x_0;
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b->ay = y_3 - 3 * y_2 + 3 * y_1 - y_0;
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#if 0
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g_debug ("Cooeficients {{%d,%d},{%d,%d},{%d,%d},{%d,%d}}",
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b->ax, b->ay, b->bx, b->by, b->cx, b->cy, b->dx, b->dy);
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#endif
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/*
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* Because of the way we do the multiplication in bezeir_t2x,y
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* these coefficients need to be at most 0x1fff; this should be the case,
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* I think, but have added this warning to catch any problems -- if it
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* triggers, we need to change those two functions a bit.
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*/
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if (b->ax > 0x1fff || b->bx > 0x1fff || b->cx > 0x1fff)
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g_warning ("Calculated coefficients will result in multiplication "
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"overflow in clutter_bezier_t2x and clutter_bezier_t2y.");
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/*
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* Sample the bezier with CBZ_T_SAMPLES and calculate length at
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* each point.
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*
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* We are working with integers here, so we use the fast sqrti function.
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*/
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length[0] = 0;
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for (t = CBZ_T_STEP, i = 1; i <= CBZ_T_SAMPLES; ++i, t += CBZ_T_STEP)
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{
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int x = _clutter_bezier_t2x (b, t);
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int y = _clutter_bezier_t2y (b, t);
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guint l = sqrti ((y - yp)*(y - yp) + (x - xp)*(x - xp));
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l += length[i-1];
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length[i] = l;
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xp = x;
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yp = y;
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}
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b->length = length[CBZ_T_SAMPLES];
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#if 0
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g_debug ("length %d", b->length);
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#endif
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}
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guint
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_clutter_bezier_get_length (const ClutterBezier *b)
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{
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return b->length;
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}
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