borgware-2d/animations/fpmath_patterns.c

568 lines
18 KiB
C

/**
* \defgroup fixedpoint Fixed-point based animated plasma patterns.
*/
/*@{*/
/**
* @file fpmath_patterns.c
* @brief Routines for drawing patterns generated by fixed-point math functions.
* @author Christian Kroll
*/
#include <assert.h>
#include <stdint.h>
#include <stddef.h>
#include "../config.h"
#include "../pixel.h"
#include "../util.h"
#include "fpmath_patterns.h"
#ifdef DOXYGEN
/**
* Low precision means that we use Q10.5 values and 16 bit types for almost
* every calculation (with multiplication and division as notable exceptions
* as they and their interim results utilize 32 bit).
*
* Use this precision mode with care as image quality will suffer
* noticeably. It produces leaner and faster code, though. This mode should
* not be used with resolutions higher than 16x16 as overflows are likely to
* occur in interim calculations.
*
* Normal precision (i.e. #undef LOW_PRECISION) conforms to Q7.8 with the
* ability to store every interim result as Q23.8. Most operations like
* square root, sine, cosine, multiplication etc. utilize 32 bit types.
*/
#define FP_LOW_PRECISION
#endif /* DOXYGEN */
#ifdef FP_LOW_PRECISION
#undef FP_LOW_PRECISION
#endif
// low precision for displays where each dimension is less than or equal to 16
#if NUM_COLS <= 16 && NUM_ROWS <= 16
#define FP_LOW_PRECISION
#endif
#ifdef FP_LOW_PRECISION
/** This is the type we expect ordinary integers to be. */
typedef int16_t ordinary_int_t;
/** This is the type which we use for fixed-point values. */
typedef int16_t fixp_t;
/** This type covers arguments of fixSin() and fixCos(). */
typedef int16_t fixp_trig_t;
/** This type covers interim results of fixed-point operations. */
typedef uint32_t fixp_interim_t;
/** This type covers interim results of the fixSqrt() function. */
typedef uint16_t ufixp_interim_t;
/** Number of bits the fixSqrt() function can handle. */
#define SQRT_BITS 16
// NOTE: If you change the following values, don't forget to adapt the sine
// lookup table as well!
/** Multiply a number by this factor to convert it to a fixed-point value.*/
#define FIX 32
/** Number of fractional bits of a value (i.e. ceil(log_2(FIX))). */
#define FIX_FRACBITS 5
/**
* The number of temporal quantization steps of the sine lookup table. It
* must be a divisor of (FIX * 2 * pi) and this divisor must be divisable by
* 4 itself. Approximate this value as close as possible to keep rounding
* errors at a minimum.
*/
#define FIX_SIN_COUNT 200
/** The rounded down quotient of (FIX * 2 * pi) and FIX_SIN_COUNT */
#define FIX_SIN_DIVIDER 1
/** Type of the lookup table elements. */
typedef uint8_t lut_t;
/**
* Lookup table of fractional parts which model the first quarter of a
* sine period. The rest of that period is calculated by mirroring those
* values. These values are intended for Q5 types.
*/
static lut_t const fix_sine_lut[FIX_SIN_COUNT / 4] =
{ 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 14,
15, 16, 17, 18, 19, 20, 20, 21,
22, 23, 23, 24, 25, 25, 26, 26,
27, 27, 28, 28, 29, 29, 30, 30,
30, 31, 31, 31, 31, 32, 32, 32,
32, 32};
#else
/** This is the type we expect ordinary integers to be. */
typedef int16_t ordinary_int_t;
/** This is the type which we use for fixed-point values. */
typedef int16_t fixp_t;
/** This type covers arguments of fixSin() and fixCos(). */
typedef int32_t fixp_trig_t;
/** This type covers interim results of fixed-point operations. */
typedef int32_t fixp_interim_t;
/** This type covers interim results of the fixSqrt() function. */
typedef uint32_t ufixp_interim_t;
/** Number of bits the fixSqrt() function can handle. */
#define SQRT_BITS 32
// NOTE: If you change the following values, don't forget to adapt the sine
// lookup table as well!
/** Multiply a number by this factor to convert it to a fixed-point value.*/
#define FIX 256
/** Number of fractional bits of a value (i.e. ceil(log_2(FIX))). */
#define FIX_FRACBITS 8
/**
* The number of temporal quantization steps of the sine lookup table. It
* must be a divisor of (FIX * 2 * pi) and this divisor must be divisable by
* 4 itself. Approximate this value as close as possible to keep rounding
* errors at a minimum.
*/
#define FIX_SIN_COUNT 200
/** The rounded down quotient of (FIX * 2 * pi) and FIX_SIN_COUNT */
#define FIX_SIN_DIVIDER 8
/** Type of the lookup table elements. */
typedef uint8_t lut_t;
/**
* Lookup table of fractional parts which model the first quarter of a
* sine period. The rest of that period is calculated by mirroring those
* values. These values are intended for Q8 types.
*/
static lut_t const fix_sine_lut[FIX_SIN_COUNT / 4] =
{ 0, 9, 17, 24, 32, 40, 48, 56,
64, 72, 79, 87, 94, 102, 109, 116,
123, 130, 137, 144, 150, 157, 163, 169,
175, 181, 186, 192, 197, 202, 207, 211,
216, 220, 224, 228, 231, 235, 238, 240,
243, 245, 247, 249, 251, 252, 253, 254,
255, 255};
#endif
/** The ordinary pi constant. */
#define PI 3.14159265358979323846
/** Fixed-point version of (pi / 2). */
#define FIX_PI_2 ((fixp_t)(PI * FIX / 2))
/** Fixed-point version of pi. */
#define FIX_PI ((fixp_t)(PI * FIX))
/** Fixed-point version of (2 * pi). */
#define FIX_2PI ((fixp_t)(2 * PI * FIX))
/**
* Scales an ordinary integer up to its fixed-point format.
* @param a An ordinary integer to be scaled up.
* @return The given value in fixed-point format.
*/
inline static fixp_t fixScaleUp(ordinary_int_t a)
{
return (fixp_t)a * FIX;
}
/**
* Scales a fixed-point value down to an ordinary integer (omitting the
* fractional part).
* @param a Fixed-point value to be scaled down to an integer.
* @return The given value as an integer.
*/
inline static ordinary_int_t fixScaleDown(fixp_t const a)
{
return a / FIX;
}
/**
* Multiplies two fixed-point values.
* @param a A multiplicand.
* @param b A multiplying factor.
* @return Product of a and b.
*/
inline static fixp_interim_t fixMul(fixp_t const a, fixp_t const b)
{
return ((fixp_interim_t)a * (fixp_interim_t)b) / FIX;
}
/**
* Divides two fixed-point values.
* @param a A dividend.
* @param b A divisor.
* @return Quotient of a and b.
*/
inline static fixp_t fixDiv(fixp_interim_t const a, fixp_interim_t const b)
{
return (a * FIX) / b;
}
/**
* Fixed-point variant of the sine function which receives a fixed-point angle
* (radian). It uses a lookup table which models the first quarter of a full
* sine period and calculates the rest from that quarter.
* @param fAngle A fixed-point value in radian.
* @return Result of the sine function normalized to a range from -FIX to FIX.
*/
static fixp_t fixSin(fixp_trig_t fAngle)
{
// convert given fixed-point angle to its corresponding quantization step
int8_t nSign = 1;
if (fAngle < 0)
{
// take advantage of sin(-x) == -sin(x) to avoid neg. operands for "%"
fAngle = -fAngle;
nSign = -1;
}
uint8_t nIndex = (fAngle / FIX_SIN_DIVIDER) % FIX_SIN_COUNT;
// now convert that quantization step to an index of our quartered array
if ((nIndex >= (FIX_SIN_COUNT / 4)))
{
if (nIndex < (FIX_SIN_COUNT / 2))
{
nIndex = (FIX_SIN_COUNT / 2 - 1) - nIndex;
}
else
{
// an angle > PI means that we have to toggle the sign of the result
nSign *= -1;
if (nIndex < (FIX_SIN_COUNT - (FIX_SIN_COUNT / 4)))
{
nIndex = nIndex - (FIX_SIN_COUNT / 2);
}
else
{
nIndex = (FIX_SIN_COUNT - 1) - nIndex;
}
}
}
assert(nIndex < (FIX_SIN_COUNT / 4));
return ((fixp_t)fix_sine_lut[nIndex]) * nSign;
}
/**
* Fixed-point variant of the cosine function which takes a fixed-point angle
* (radian). It adds FIX_PI_2 to the given angle and consults the fixSin()
* function for the final result.
* @param fAngle A fixed-point value in radian.
* @return Result of the cosine function normalized to a range from -FIX to FIX.
*/
static fixp_t fixCos(fixp_trig_t const fAngle)
{
return fixSin(fAngle + FIX_PI_2);
}
/**
* Fixed-point square root algorithm as proposed by Ken Turkowski:
* http://www.realitypixels.com/turk/computergraphics/FixedSqrt.pdf
* @param a The radicant we want the square root of.
* @return The square root of the given value.
*/
static fixp_t fixSqrt(ufixp_interim_t const a)
{
ufixp_interim_t nRoot, nRemainingHigh, nRemainingLow, nTestDiv, nCount;
nRoot = 0; // clear root
nRemainingHigh = 0; // clear high part of partial remainder
nRemainingLow = a; // get argument into low part of partial remainder
nCount = (SQRT_BITS / 2 - 1) + (FIX_FRACBITS >> 1); // load loop counter
do
{
nRemainingHigh =
(nRemainingHigh << 2) | (nRemainingLow >> (SQRT_BITS - 2));
nRemainingLow <<= 2; // get 2 bits of the argument
nRoot <<= 1; // get ready for the next bit in the root
nTestDiv = (nRoot << 1) + 1; // test radical
if (nRemainingHigh >= nTestDiv)
{
nRemainingHigh -= nTestDiv;
nRoot++;
}
} while (nCount-- != 0);
return (fixp_t)nRoot;
}
/**
* Calculates the distance between two points.
* @param x1 x-coordinate of the first point
* @param y1 y-coordinate of the first point
* @param x2 x-coordinate of the second point
* @param y2 y-coordinate of the second point
* @return The distance between the given points.
*/
static fixp_t fixDist(fixp_t const x1,
fixp_t const y1,
fixp_t const x2,
fixp_t const y2)
{
return fixSqrt(fixMul((x1 - x2), (x1 - x2)) + fixMul((y1 - y2), (y1 - y2)));
}
/**
* This pointer type covers functions which return a brightness value for the
* given coordinates and a "step" value. Applied to all coordinates of the
* borg's display this actually results in a more or less beautiful pattern.
* @param x x-coordinate
* @param y y-coordinate
* @param t A step value which changes for each frame, allowing for animations.
* @param r A pointer to persistent data required by the pattern function.
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
typedef unsigned char (*fpmath_pattern_func_t)(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r);
/**
* Draws an animated two dimensional graph for a given function f(x, y, t).
* @param t_start A start value for the function's step variable.
* @param t_stop A stop value for the function's step variable.
* @param t_delta Value by which the function's step variable gets incremented.
* @param frame_delay The frame delay in milliseconds.
* @param fpPattern Function which generates a pattern depending on x, y and t.
* @param r A pointer to persistent data required by the fpPattern function.
*/
static void fixDrawPattern(fixp_t const t_start,
fixp_t const t_stop,
fixp_t const t_delta,
int const frame_delay,
fpmath_pattern_func_t fpPattern,
void *r)
{
// off-screen buffer
unsigned char pOffScreen[NUMPLANE + 1][NUM_ROWS][LINEBYTES];
for (fixp_t t = t_start; t < t_stop; t += t_delta)
{
// For performance reasons the pattern is drawn to an off-screen buffer
// without distributing bits of higher planes down to lower ones.
ptrdiff_t nRowColOffset = 0;
for (unsigned char y = 0; y < UNUM_ROWS; ++y)
{
for (unsigned char x = 0; x < (LINEBYTES * 8u); ++x)
{
// Since multidimensional subscript expressions are rather
// expensive, we just resolve the first dimension (which
// represents the plane) and add an offset that correlates to
// the currently processed row and column.
*(&pOffScreen[fpPattern(x, y, t, r)][0][0] + nRowColOffset) |=
shl_table[x % 8u];
// increment the offset after completion of a byte
if ((x % 8u) == 7u)
{
nRowColOffset++;
}
}
}
// one byte behind the frame buffer
unsigned char *pPixmap =
(&pixmap[NUMPLANE - 1][NUM_ROWS - 1][LINEBYTES - 1]) + 1;
// one byte behind the off-screen buffer
unsigned char *pOffscreenDistHigh =
(&pOffScreen[NUMPLANE][NUM_ROWS - 1][LINEBYTES - 1]) + 1;
// one byte behind the second last plane of the off-screen buffer
unsigned char *pOffscreenDistLow =
(&pOffScreen[NUMPLANE - 1][NUM_ROWS - 1][LINEBYTES - 1]) + 1;
// Here we transcribe the off-screen contents to the actual frame buffer
// by distributing down 8 bits in parallel per iteration. We start at
// the end of both buffers and move backwards through their space.
// The pre-decrement operator is used so that GCC utilizes the AVR's
// built-in pre-decrement variants of the "ld" and "st" instructions.
while (pPixmap != &pixmap[0][0][0]) // stop at the beginning
{
// actually draw off-screen contents
*(--pPixmap) = *(--pOffscreenDistHigh);
// distribute bits down to the next lower plane
*(--pOffscreenDistLow) |= *pOffscreenDistHigh;
// clear already drawn off-screen contents
*pOffscreenDistHigh = 0;
}
// wait a moment to ensure that the current frame is visible
wait(frame_delay);
}
}
#ifdef ANIMATION_PLASMA
/**
* This type maintains values relevant for the Plasma animation which need to be
* persistent over consecutive invocations.
* @see fixAnimPlasma()
*/
typedef struct fixp_plasma_s
{
/**
* This array holds column dependent results of the first internal pattern
* function. Those results only need to be calculated for the first row of
* the current frame and are then reused for the remaining rows.
*/
fixp_t fFunc1[LINEBYTES * 8u];
/**
* This value is part of the formula for the second internal pattern
* function. It needs to be calculated only once per frame.
*/
fixp_t fFunc2CosArg;
/**
* This value is part of the formula for the second internal pattern
* function. It needs to be calculated only once per frame.
*/
fixp_t fFunc2SinArg;
} fixp_plasma_t;
/**
* Generates a plasma like pattern (sort of... four shades of grey are pretty
* scarce for a neat plasma animation). This is realized by superimposing two
* functions which generate independent patterns for themselves.
*
* The first function draws horizontally moving waves and the second function
* draws zoomed-in radiating curls. Together they create a wobbly, plasma like
* pattern.
*
* @param x x-coordinate
* @param y y-coordinate
* @param t A Step value which changes for each frame, allowing for animations.
* @param r A pointer to persistent interim results.
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
static unsigned char fixAnimPlasma(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r)
{
assert(x < NUM_COLS);
assert(y < NUM_ROWS);
// scaling factor
static fixp_t const fPlasmaX = (2 * PI * FIX) / NUM_COLS;
// reentrant data
fixp_plasma_t *const p = (fixp_plasma_t *)r;
if (x == 0 && y == 0)
{
p->fFunc2CosArg = NUM_ROWS * fixCos(t) + fixScaleUp(NUM_ROWS);
p->fFunc2SinArg = NUM_COLS * fixSin(t) + fixScaleUp(NUM_COLS);
for (unsigned char i = LINEBYTES * 8u; i--;)
{
p->fFunc1[i] = fixSin(fixMul(fixScaleUp(i), fPlasmaX) + t);
}
}
fixp_t const fFunc2 = fixSin(fixMul(fixDist(fixScaleUp(x), fixScaleUp(y),
p->fFunc2SinArg, p->fFunc2CosArg), fPlasmaX));
unsigned char const nRes = (unsigned char)(fixMul(p->fFunc1[x] + fFunc2 +
fixScaleUp(2), ((NUMPLANE + 1) / 4.0 - 0.05) * FIX)) / FIX;
assert (nRes <= NUMPLANE);
return nRes;
}
/**
* Starting point for the Plasma animation.
*/
void plasma(void)
{
fixp_plasma_t r;
#ifndef __AVR__
fixDrawPattern(0, fixScaleUp(75), 0.1 * FIX, 15, fixAnimPlasma, &r);
#else
#ifndef FP_PLASMA_DELAY
#define FP_PLASMA_DELAY 1
#endif
fixDrawPattern(0, fixScaleUp(60), 0.1 * FIX,
FP_PLASMA_DELAY, fixAnimPlasma, &r);
#endif /* __AVR__ */
}
#endif /* ANIMATION_PLASMA */
#ifdef ANIMATION_PSYCHEDELIC
/**
* This type maintains values relevant for the Psychedelic animation which need
* to be persistent over consecutive invocations.
*/
typedef struct fixp_psychedelic_s
{
fixp_t fCos; /**< One of the column factors of the curl. */
fixp_t fSin; /**< One of the row factors of the curl. */
fixp_interim_t ft10; /**< A value involved in rotating the curl's center. */
} fixp_psychedelic_t;
/**
* Generates flowing circular waves with a rotating center.
* @param x x-coordinate
* @param y y-coordinate
* @param t A step value which changes for each frame, allowing for animations.
* @param r A pointer to persistent interim results.
* @return The brightness value (0 < n <= NUM_PLANES) of the given coordinate.
*/
static unsigned char fixAnimPsychedelic(unsigned char const x,
unsigned char const y,
fixp_t const t,
void *const r)
{
assert(x < NUM_COLS);
assert(y < NUM_ROWS);
fixp_psychedelic_t *p = (fixp_psychedelic_t *)r;
if (x == 0 && y == 0)
{
p->fCos = NUM_COLS/2 * fixCos(t);
p->fSin = NUM_ROWS/2 * fixSin(t);
p->ft10 = fixMul(t, fixScaleUp(10));
}
unsigned char const nResult =
(unsigned char)(fixMul(fixSin(fixDist(fixScaleUp(x), fixScaleUp(y),
p->fCos, p->fSin) - p->ft10) + fixScaleUp(1),
(fixp_t)((NUMPLANE - 1.05) * FIX))) / FIX;
assert(nResult <= NUMPLANE);
return nResult;
}
/**
* Starting point for the Psychedelic animation.
*/
void psychedelic(void)
{
fixp_psychedelic_t r;
#ifndef __AVR__
fixDrawPattern(0, fixScaleUp(75), 0.1 * FIX, 30, fixAnimPsychedelic, &r);
#else
#ifndef FP_PSYCHO_DELAY
#define FP_PSYCHO_DELAY 15
#endif
fixDrawPattern(0, fixScaleUp(60), 0.1 * FIX, FP_PSYCHO_DELAY,
fixAnimPsychedelic, &r);
#endif /* __AVR__ */
}
#endif /* ANIMATION_PSYCHEDELIC */
/*@}*/