159b2e6871c65f58fdad78cd7229c292f6a177578Scott Bartapackage jme3tools.android; 259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 359b2e6871c65f58fdad78cd7229c292f6a177578Scott Bartaimport java.util.Random; 459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta/** 659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Fixed point maths class. This can be tailored for specific needs by 759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * changing the bits allocated to the 'fraction' part (see <code>FIXED_POINT 859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * </code>, which would also require <code>SIN_PRECALC</code> and <code> 959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * COS_PRECALC</code> updating). 1059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 1159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * <p><a href="http://blog.numfum.com/2007/09/java-fixed-point-maths.html"> 1259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * http://blog.numfum.com/2007/09/java-fixed-point-maths.html</a></p> 1359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 1459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @version 1.0 1559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @author CW 1659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 1759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @deprecated Most devices with OpenGL ES 2.0 have an FPU. Please use 1859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * floats instead of this class for decimal math. 1959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 2059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta@Deprecated 2159b2e6871c65f58fdad78cd7229c292f6a177578Scott Bartapublic final class Fixed { 2259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 2359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 2459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Number of bits used for 'fraction'. 2559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 2659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static final int FIXED_POINT = 16; 2759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 2859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Decimal one as represented by the Fixed class. 2959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 3059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static final int ONE = 1 << FIXED_POINT; 3159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 3259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Half in fixed point. 3359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 3459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static final int HALF = ONE >> 1; 3559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 3659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Quarter circle resolution for trig functions (should be a power of 3759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * two). This is the number of discrete steps in 90 degrees. 3859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 3959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static final int QUARTER_CIRCLE = 64; 4059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 4159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Mask used to limit angles to one revolution. If a quarter circle is 64 4259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * (i.e. 90 degrees is broken into 64 steps) then the mask is 255. 4359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 4459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static final int FULL_CIRCLE_MASK = QUARTER_CIRCLE * 4 - 1; 4559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 4659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * The trig table is generated at a higher precision than the typical 4759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 16.16 format used for the rest of the fixed point maths. The table 4859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * values are then shifted to match the actual fixed point used. 4959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 5059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int TABLE_SHIFT = 30; 5159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 5259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Equivalent to: sin((2 * PI) / (QUARTER_CIRCLE * 4)) 5359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * <p> 5459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Note: if either QUARTER_CIRCLE or TABLE_SHIFT is changed this value 5559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * will need recalculating (put the above formular into a calculator set 5659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * radians, then shift the result by <code>TABLE_SHIFT</code>). 5759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 5859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int SIN_PRECALC = 26350943; 5959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 6059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Equivalent to: cos((2 * PI) / (QUARTER_CIRCLE * 4)) * 2 6159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 6259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Note: if either QUARTER_CIRCLE or TABLE_SHIFT is changed this value 6359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * will need recalculating ((put the above formular into a calculator set 6459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * radians, then shift the result by <code>TABLE_SHIFT</code>). 6559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 6659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int COS_PRECALC = 2146836866; 6759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 6859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * One quarter sine wave as fixed point values. 6959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 7059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int[] SINE_TABLE = new int[QUARTER_CIRCLE + 1]; 7159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 7259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Scale value for indexing ATAN_TABLE[]. 7359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 7459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int ATAN_SHIFT; 7559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 7659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Reverse atan lookup table. 7759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 7859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final byte[] ATAN_TABLE; 7959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 8059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * ATAN_TABLE.length 8159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 8259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int ATAN_TABLE_LEN; 8359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 8459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /* 8559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Generates the tables and fills in any remaining static ints. 8659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 8759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta static { 8859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta // Generate the sine table using recursive synthesis. 8959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta SINE_TABLE[0] = 0; 9059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta SINE_TABLE[1] = SIN_PRECALC; 9159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int n = 2; n < QUARTER_CIRCLE + 1; n++) { 9259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta SINE_TABLE[n] = (int) (((long) SINE_TABLE[n - 1] * COS_PRECALC) >> TABLE_SHIFT) - SINE_TABLE[n - 2]; 9359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 9459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta // Scale the values to the fixed point format used. 9559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int n = 0; n < QUARTER_CIRCLE + 1; n++) { 9659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta SINE_TABLE[n] = SINE_TABLE[n] + (1 << (TABLE_SHIFT - FIXED_POINT - 1)) >> TABLE_SHIFT - FIXED_POINT; 9759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 9859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 9959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta // Calculate a shift used to scale atan lookups 10059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int rotl = 0; 10159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int tan0 = tan(0); 10259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int tan1 = tan(1); 10359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta while (rotl < 32) { 10459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if ((tan1 >>= 1) > (tan0 >>= 1)) { 10559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta rotl++; 10659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 10759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta break; 10859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 10959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 11059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta ATAN_SHIFT = rotl; 11159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta // Create the a table of tan values 11259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int[] lut = new int[QUARTER_CIRCLE]; 11359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int n = 0; n < QUARTER_CIRCLE; n++) { 11459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta lut[n] = tan(n) >> rotl; 11559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 11659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta ATAN_TABLE_LEN = lut[QUARTER_CIRCLE - 1]; 11759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta // Then from the tan values create a reverse lookup 11859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta ATAN_TABLE = new byte[ATAN_TABLE_LEN]; 11959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (byte n = 0; n < QUARTER_CIRCLE - 1; n++) { 12059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int min = lut[n]; 12159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int max = lut[n + 1]; 12259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int i = min; i < max; i++) { 12359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta ATAN_TABLE[i] = n; 12459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 12559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 12659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 12759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 12859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * How many decimal places to use when converting a fixed point value to 12959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * a decimal string. 13059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 13159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @see #toString 13259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 13359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int STRING_DECIMAL_PLACES = 2; 13459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 13559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Value to add in order to round down a fixed point number when 13659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * converting to a string. 13759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 13859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static final int STRING_DECIMAL_PLACES_ROUND; 13959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 14059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta static { 14159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int i = 10; 14259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int n = 1; n < STRING_DECIMAL_PLACES; n++) { 14359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta i *= i; 14459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 14559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (STRING_DECIMAL_PLACES == 0) { 14659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta STRING_DECIMAL_PLACES_ROUND = ONE / 2; 14759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 14859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta STRING_DECIMAL_PLACES_ROUND = ONE / (2 * i); 14959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 15059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 15159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 15259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Random number generator. The standard <code>java.utll.Random</code> is 15359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * used since it is available to both J2ME and J2SE. If a guaranteed 15459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * sequence is required this would not be adequate. 15559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 15659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private static Random rng = null; 15759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 15859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 15959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Fixed can't be instantiated. 16059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 16159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta private Fixed() { 16259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 16359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 16459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 16559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns an integer as a fixed point value. 16659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 16759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int intToFixed(int n) { 16859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return n << FIXED_POINT; 16959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 17059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 17159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 17259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns a fixed point value as a float. 17359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 17459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static float fixedToFloat(int i) { 17559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta float fp = i; 17659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta fp = fp / ((float) ONE); 17759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return fp; 17859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 17959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 18059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 18159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns a float as a fixed point value. 18259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 18359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int floatToFixed(float fp) { 18459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (int) (fp * ((float) ONE)); 18559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 18659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 18759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 18859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Converts a fixed point value into a decimal string. 18959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 19059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static String toString(int n) { 19159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta StringBuffer sb = new StringBuffer(16); 19259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta sb.append((n += STRING_DECIMAL_PLACES_ROUND) >> FIXED_POINT); 19359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta sb.append('.'); 19459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n &= ONE - 1; 19559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta for (int i = 0; i < STRING_DECIMAL_PLACES; i++) { 19659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n *= 10; 19759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta sb.append((n / ONE) % 10); 19859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 19959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return sb.toString(); 20059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 20159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 20259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 20359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Multiplies two fixed point values and returns the result. 20459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 20559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int mul(int a, int b) { 20659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (int) ((long) a * (long) b >> FIXED_POINT); 20759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 20859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 20959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 21059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Divides two fixed point values and returns the result. 21159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 21259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int div(int a, int b) { 21359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (int) (((long) a << FIXED_POINT * 2) / (long) b >> FIXED_POINT); 21459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 21559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 21659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 21759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Sine of an angle. 21859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 21959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @see #QUARTER_CIRCLE 22059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 22159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int sin(int n) { 22259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n &= FULL_CIRCLE_MASK; 22359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE * 2) { 22459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE) { 22559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return SINE_TABLE[n]; 22659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 22759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return SINE_TABLE[QUARTER_CIRCLE * 2 - n]; 22859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 22959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 23059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE * 3) { 23159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -SINE_TABLE[n - QUARTER_CIRCLE * 2]; 23259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 23359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -SINE_TABLE[QUARTER_CIRCLE * 4 - n]; 23459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 23559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 23659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 23759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 23859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 23959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Cosine of an angle. 24059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 24159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @see #QUARTER_CIRCLE 24259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 24359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int cos(int n) { 24459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n &= FULL_CIRCLE_MASK; 24559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE * 2) { 24659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE) { 24759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return SINE_TABLE[QUARTER_CIRCLE - n]; 24859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 24959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -SINE_TABLE[n - QUARTER_CIRCLE]; 25059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 25159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 25259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < QUARTER_CIRCLE * 3) { 25359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -SINE_TABLE[QUARTER_CIRCLE * 3 - n]; 25459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 25559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return SINE_TABLE[n - QUARTER_CIRCLE * 3]; 25659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 25759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 25859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 25959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 26059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 26159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Tangent of an angle. 26259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * 26359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * @see #QUARTER_CIRCLE 26459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 26559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int tan(int n) { 26659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return div(sin(n), cos(n)); 26759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 26859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 26959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 27059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the arc tangent of an angle. 27159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 27259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int atan(int n) { 27359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n = n + (1 << (ATAN_SHIFT - 1)) >> ATAN_SHIFT; 27459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n < 0) { 27559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n <= -ATAN_TABLE_LEN) { 27659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -(QUARTER_CIRCLE - 1); 27759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 27859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -ATAN_TABLE[-n]; 27959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } else { 28059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n >= ATAN_TABLE_LEN) { 28159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return QUARTER_CIRCLE - 1; 28259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 28359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return ATAN_TABLE[n]; 28459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 28559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 28659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 28759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 28859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the polar angle of a rectangular coordinate. 28959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 29059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int atan(int x, int y) { 29159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int n = atan(div(x, abs(y) + 1)); // kludge to prevent ArithmeticException 29259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (y > 0) { 29359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return n; 29459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 29559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (y < 0) { 29659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (x < 0) { 29759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -QUARTER_CIRCLE * 2 - n; 29859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 29959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (x > 0) { 30059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return QUARTER_CIRCLE * 2 - n; 30159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 30259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return QUARTER_CIRCLE * 2; 30359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 30459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (x > 0) { 30559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return QUARTER_CIRCLE; 30659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 30759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return -QUARTER_CIRCLE; 30859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 30959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 31059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 31159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Rough calculation of the hypotenuse. Whilst not accurate it is very fast. 31259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * <p> 31359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Derived from a piece in Graphics Gems. 31459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 31559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int hyp(int x1, int y1, int x2, int y2) { 31659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if ((x2 -= x1) < 0) { 31759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta x2 = -x2; 31859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 31959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if ((y2 -= y1) < 0) { 32059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta y2 = -y2; 32159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 32259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return x2 + y2 - (((x2 > y2) ? y2 : x2) >> 1); 32359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 32459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 32559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 32659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Fixed point square root. 32759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * <p> 32859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Derived from a 1993 Usenet algorithm posted by Christophe Meessen. 32959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 33059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int sqrt(int n) { 33159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n <= 0) { 33259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return 0; 33359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 33459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta long sum = 0; 33559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta int bit = 0x40000000; 33659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta while (bit >= 0x100) { // lower values give more accurate results 33759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta long tmp = sum | bit; 33859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (n >= tmp) { 33959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n -= tmp; 34059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta sum = tmp + bit; 34159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 34259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta bit >>= 1; 34359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta n <<= 1; 34459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 34559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (int) (sum >> 16 - (FIXED_POINT / 2)); 34659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 34759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 34859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 34959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the absolute value. 35059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 35159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int abs(int n) { 35259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (n < 0) ? -n : n; 35359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 35459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 35559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 35659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the sign of a value, -1 for negative numbers, otherwise 1. 35759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 35859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int sgn(int n) { 35959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (n < 0) ? -1 : 1; 36059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 36159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 36259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 36359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the minimum of two values. 36459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 36559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int min(int a, int b) { 36659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (a < b) ? a : b; 36759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 36859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 36959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 37059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the maximum of two values. 37159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 37259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int max(int a, int b) { 37359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (a > b) ? a : b; 37459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 37559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 37659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 37759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Clamps the value n between min and max. 37859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 37959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int clamp(int n, int min, int max) { 38059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (n < min) ? min : (n > max) ? max : n; 38159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 38259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 38359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 38459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Wraps the value n between 0 and the required limit. 38559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 38659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int wrap(int n, int limit) { 38759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return ((n %= limit) < 0) ? limit + n : n; 38859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 38959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 39059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 39159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the nearest int to a fixed point value. Equivalent to <code> 39259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Math.round()</code> in the standard library. 39359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 39459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int round(int n) { 39559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return n + HALF >> FIXED_POINT; 39659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 39759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 39859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 39959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the nearest int rounded down from a fixed point value. 40059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Equivalent to <code>Math.floor()</code> in the standard library. 40159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 40259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int floor(int n) { 40359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return n >> FIXED_POINT; 40459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 40559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 40659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 40759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns the nearest int rounded up from a fixed point value. 40859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Equivalent to <code>Math.ceil()</code> in the standard library. 40959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 41059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int ceil(int n) { 41159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return n + (ONE - 1) >> FIXED_POINT; 41259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 41359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 41459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 41559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns a fixed point value greater than or equal to decimal 0.0 and 41659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * less than 1.0 (in 16.16 format this would be 0 to 65535 inclusive). 41759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 41859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int rand() { 41959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta if (rng == null) { 42059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta rng = new Random(); 42159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 42259b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return rng.nextInt() >>> (32 - FIXED_POINT); 42359b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 42459b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta 42559b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta /** 42659b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta * Returns a random number between 0 and <code>n</code> (exclusive). 42759b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta */ 42859b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta public static int rand(int n) { 42959b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta return (rand() * n) >> FIXED_POINT; 43059b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta } 43159b2e6871c65f58fdad78cd7229c292f6a177578Scott Barta}