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8b977e9046
It has been inofficially deprecated for years, is known to cause issues with valgrind and potentially hides memory corruption. Lets stop using it. Part-of: <https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/1512>
515 lines
14 KiB
C
515 lines
14 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-build-config.h"
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#include <glib.h>
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#include <string.h>
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#include "clutter-bezier.h"
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#include "clutter-debug.h"
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/*
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* We have some experimental code here to allow for constant velocity
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* movement of actors along the bezier path, this macro enables it.
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*/
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#undef CBZ_L2T_INTERPOLATION
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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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#ifdef CBZ_L2T_INTERPOLATION
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/*
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* coefficients for the L -> t bezier; these are calculated from fixed
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* point input, and more specifically numbers that have been normalised
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* to fit <0,1>, so these are also fixed point, and we can used the
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* _FixedT type here.
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*/
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_FixedT La;
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_FixedT Lb;
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_FixedT Lc;
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/* _FixedT Ld; == 0 */
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#endif
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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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ClutterBezier *
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_clutter_bezier_clone_and_move (const ClutterBezier *b, gint x, gint y)
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{
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ClutterBezier * b2 = _clutter_bezier_new ();
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memcpy (b2, b, sizeof (ClutterBezier));
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b2->dx += x;
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b2->dy += y;
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return b2;
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}
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#ifdef CBZ_L2T_INTERPOLATION
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/*
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* L is relative advance along the bezier curve from interval <0,1>
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*/
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static _FixedT
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_clutter_bezier_L2t (const ClutterBezier *b, _FixedT L)
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{
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_FixedT t = CBZ_T_MUL (b->La, CBZ_T_POW3(L))
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+ CBZ_T_MUL (b->Lb, CBZ_T_POW2(L))
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+ CBZ_T_MUL (b->Lc, L);
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if (t > CBZ_T_ONE)
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t = CBZ_T_ONE;
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else if (t < 0)
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t = 0;
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return t;
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}
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#endif
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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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#ifdef CBZ_L2T_INTERPOLATION
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_FixedT t = clutter_bezier_L2t (b, L);
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#else
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_FixedT t = L;
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#endif
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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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#ifdef CBZ_L2T_INTERPOLATION
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int j, k;
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_FixedT L;
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_FixedT t_equalized [CBZ_T_SAMPLES + 1];
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#endif
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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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#ifdef CBZ_L2T_INTERPOLATION
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/*
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* Now normalize the length values, converting them into _FixedT
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*/
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for (i = 0; i <= CBZ_T_SAMPLES; ++i)
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{
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length[i] = (length[i] << CBZ_T_Q) / b->length;
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}
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/*
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* Now generate a L -> t table such that the L will equidistant
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* over <0,1>
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*/
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t_equalized[0] = 0;
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for (i = 1, j = 1, L = CBZ_L_STEP; i < CBZ_T_SAMPLES; ++i, L += CBZ_L_STEP)
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{
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_FixedT l1, l2;
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_FixedT d1, d2, d;
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_FixedT t1, t2;
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/* find the band for our L */
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for (k = j; k < CBZ_T_SAMPLES; ++k)
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{
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if (L < length[k])
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break;
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}
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/*
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* Now we know that L is from (length[k-1],length[k]>
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* We remember k-1 in order not to have to iterate over the
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* whole length array in the next iteration of the main loop
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*/
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j = k - 1;
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/*
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* Now interpolate equlised t as a weighted average
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*/
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l1 = length[k-1];
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l2 = length[k];
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d1 = l2 - L;
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d2 = L - l1;
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d = l2 - l1;
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t1 = (k - 1) * CBZ_T_STEP;
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t2 = k * CBZ_T_STEP;
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t_equalized[i] = (t1*d1 + t2*d2)/d;
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if (t_equalized[i] < t_equalized[i-1])
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g_debug ("wrong t: L %f, l1 %f, l2 %f, t1 %f, t2 %f",
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(double) (L)/(double)CBZ_T_ONE,
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(double) (l1)/(double)CBZ_T_ONE,
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(double) (l2)/(double)CBZ_T_ONE,
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(double) (t1)/(double)CBZ_T_ONE,
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(double) (t2)/(double)CBZ_T_ONE);
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}
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t_equalized[CBZ_T_SAMPLES] = CBZ_T_ONE;
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/* We now fit a bezier -- at this stage, do a single fit through our values
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* at 0, 1/3, 2/3 and 1
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*
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* FIXME -- do we need to use a better fitting approach to choose the best
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* beziere. The actual curve we acquire this way is not too bad shapwise,
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* but (probably due to rounding errors) the resulting curve no longer
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* satisfies the necessary condition that for L2 > L1, t2 > t1, which
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* causes oscilation.
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*/
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#if 0
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/*
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* These are the control points we use to calculate the curve coefficients
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* for bezier t(L); these are not needed directly, but are implied in the
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* calculations below.
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*
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* (p0 is 0,0, and p3 is 1,1)
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*/
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p1 = (18 * t_equalized[CBZ_T_SAMPLES/3] -
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9 * t_equalized[2*CBZ_T_SAMPLES/3] +
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2 << CBZ_T_Q) / 6;
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p2 = (18 * t_equalized[2*CBZ_T_SAMPLES/3] -
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9 * t_equalized[CBZ_T_SAMPLES/3] -
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(5 << CBZ_T_Q)) / 6;
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#endif
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b->Lc = (18 * t_equalized[CBZ_T_SAMPLES/3] -
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9 * t_equalized[2*CBZ_T_SAMPLES/3] +
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(2 << CBZ_T_Q)) >> 1;
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b->Lb = (36 * t_equalized[2*CBZ_T_SAMPLES/3] -
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45 * t_equalized[CBZ_T_SAMPLES/3] -
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(9 << CBZ_T_Q)) >> 1;
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b->La = ((27 * (t_equalized[CBZ_T_SAMPLES/3] -
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t_equalized[2*CBZ_T_SAMPLES/3]) +
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(7 << CBZ_T_Q)) >> 1) + CBZ_T_ONE;
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g_debug ("t(1/3) %f, t(2/3) %f",
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(double)t_equalized[CBZ_T_SAMPLES/3]/(double)CBZ_T_ONE,
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(double)t_equalized[2*CBZ_T_SAMPLES/3]/(double)CBZ_T_ONE);
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g_debug ("L -> t coefficients: %f, %f, %f",
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(double)b->La/(double)CBZ_T_ONE,
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(double)b->Lb/(double)CBZ_T_ONE,
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(double)b->Lc/(double)CBZ_T_ONE);
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/*
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* For debugging, you can load these values into a spreadsheet and graph
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* them to see how well the approximation matches the data
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*/
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for (i = 0; i < CBZ_T_SAMPLES; ++i)
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{
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g_print ("%f, %f, %f\n",
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(double)(i*CBZ_T_STEP)/(double)CBZ_T_ONE,
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(double)(t_equalized[i])/(double)CBZ_T_ONE,
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(double)(clutter_bezier_L2t(b,i*CBZ_T_STEP))/(double)CBZ_T_ONE);
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}
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#endif
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}
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|
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/*
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* Moves a control point at indx to location represented by knot
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*/
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void
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_clutter_bezier_adjust (ClutterBezier * b, ClutterKnot * knot, guint indx)
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|
{
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guint x[4], y[4];
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|
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g_assert (indx < 4);
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|
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x[0] = b->dx;
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y[0] = b->dy;
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|
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x[1] = b->cx / 3 + x[0];
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y[1] = b->cy / 3 + y[0];
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|
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x[2] = b->bx / 3 + b->cx + x[1];
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y[2] = b->by / 3 + b->cy + y[1];
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|
|
|
x[3] = b->ax + x[0] + b->cx + b->bx;
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|
y[3] = b->ay + y[0] + b->cy + b->by;
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|
|
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x[indx] = knot->x;
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|
y[indx] = knot->y;
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|
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|
_clutter_bezier_init (b, x[0], y[0], x[1], y[1], x[2], y[2], x[3], y[3]);
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|
}
|
|
|
|
guint
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|
_clutter_bezier_get_length (const ClutterBezier *b)
|
|
{
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|
return b->length;
|
|
}
|