public static Accum MakeAccum(long val)
{
Accum k = new Accum();
k.longValue = val;
return(k);
}
public static Accum Sin(Accum x)
{
if (!tablesGenerated)
{
GenerateTables();
}
long xVal = x.Value;
while (xVal > PI_2.Value)
{
xVal -= PI_2.Value;
}
while (xVal < 0)
{
xVal += PI_2.Value;
}
long x1 = (long)(Math.Floor(((double)xVal / Accum.FracUnit) / (Math.PI * 2 / SineLUTSize))), //(Floor (xVal / (PI_2 / SineLUTSize))),
x2 = x1 + 1;
Accum y1 = SineLUT [x1],
y2 = SineLUT [x2],
y = y1 + (y2 - y1) * (x * new Accum(SineLUTSize) / PI_2 - new Accum(x1));
return(y1);
}
/// <summary>
/// Scales the Vector3k to unit length.
/// </summary>
public void Normalize()
{
Accum scale = Accum.One / this.Length;
x *= scale;
y *= scale;
z *= scale;
}
/// <summary>
/// Rounds a number upwards to the next integer. (Towards positive infinity)
/// </summary>
/// <param name="x">The number to round.</param>
/// <returns>Returns x rounded upwards to the next integer.</returns>
public static Accum Ceil(Accum x)
{
return(Accum.MakeAccum(
(x.Value < 0) ?
(x.Value & unchecked ((long)0xFFFFFFFFFFFF0000)) :
((x.Value + (Accum.FracUnit - 1)) & unchecked ((long)0xFFFFFFFFFFFF0000))
));
}
public static Vector3k operator /(double val, Vector3k vec)
{
var valAccum = new Accum(val);
vec.x /= valAccum;
vec.y /= valAccum;
vec.z /= valAccum;
return(vec);
}
public static Vector3k operator +(long val, Vector3k vec)
{
var valAccum = new Accum(val);
vec.x += valAccum;
vec.y += valAccum;
vec.z += valAccum;
return(vec);
}
public static Vector3k operator -(int val, Vector3k vec)
{
var valAccum = new Accum(val);
vec.x -= valAccum;
vec.y -= valAccum;
vec.z -= valAccum;
return(vec);
}
// Sin/Cos: pi*2: 411774; LUT size: 131072;
// LUT generation
public static void GenerateTables()
{
for (int i = 0; i < SineLUT.Length; i++)
{
SineLUT [i] = new Accum(Math.Sin((Math.PI * 2 / SineLUTSize) * i));
}
tablesGenerated = true;
}
// Multiplication
public static Vector3k operator *(Vector3k vec, double val)
{
var valAccum = new Accum(val);
vec.x *= valAccum;
vec.y *= valAccum;
vec.z *= valAccum;
return(vec);
}
/// <summary>
/// Returns x to the nth potency
/// </summary>
/// <param name="x">A number</param>
/// <param name="n">An exponent</param>
public static Accum Pow(Accum x, int n)
{
Accum ret = x;
for (; n > 0; n--)
{
ret.Value *= x.Value;
}
return(ret);
}
// Square root
/// <summary>
/// Returns the square root of a number
/// </summary>
/// <param name="x">A number</param>
public static Accum Sqrt(Accum x)
{
if (x == Accum.One)
{
return(new Accum(Accum.FracUnit));
}
if (x <= Accum.Zero)
{
return(Accum.Zero);
}
long val = 150 * Accum.FracUnit,
xVal = x.Value;
for (int i = 0; i < 15; i++)
{
val = (val + Accum.SafeDivision(xVal, val)) >> 1;
}
return(Accum.MakeAccum(val));
}
public static Accum WrapAngle(Accum x)
{
const int val = 360 << 16; // Just to make sure it doesn't calculate 360 << 16 on every WrapAngle call...
return(Accum.MakeAccum(x.Value % val));
}
/// <summary>
/// Truncates a number, dropping the fractional part.
/// </summary>
/// <param name="x">The number to truncate</param>
/// <returns>Returns x without the fractional part</returns>
public static Accum Truncate(Accum x)
{
return(new Accum(x.Value & 0xFFFF0000));
}
public Vector3k(Accum newX, Accum newY, Accum newZ)
{
x = newX;
y = newY;
z = newZ;
}
/// <summary>
/// Rounds a number to the nearest integer.
/// </summary>
/// <param name="x">The number to round.</param>
/// <returns>Returns x rounded to the nearest integer.</returns>
public static Accum Round(Accum x)
{
return(new Accum((x.Value + (Accum.FracUnit / 2)) & 0xFFFF0000));
}
// Potentiation (?)
/// <summary>
/// Returns the square of a number
/// </summary>
/// <param name="x">A number</param>
public static Accum Square(Accum x)
{
return(x * x);
}
public Accum(Accum val)
{
longValue = val.longValue;
}
/*public static Accum AtanDegrees (Accum x) { return DegreesToRadians (Atan (x)); }
* public static Accum Atan2Degrees (Accum x, Accum y) { return DegreesToRadians (Atan2 (x, y); }*/
#endregion
#region Basic math functions
// Absolute
/// <summary>
/// Returns the absolute value of a number
/// </summary>
/// <param name="x">A number</param>
public static Accum Abs(Accum val)
{
return(val.Value < 0 ? -val : val);
}
public static Accum CosDegrees(Accum x)
{
return(Sin(DegreesToRadians(x) + PIOver2));
}
public static Accum SinDegrees(Accum x)
{
return(Sin(DegreesToRadians(x)));
}
// Clamping
/// <summary>
/// Clamps a number between a minimum and a maximum.
/// </summary>
/// <param name="n">The number to clamp.</param>
/// <param name="min">The minimum allowed value.</param>
/// <param name="max">The maximum allowed value.</param>
/// <returns>min, if n is lower than min; max, if n is higher than max; n otherwise.</returns>
public static Accum Clamp(Accum n, Accum min, Accum max)
{
return(Accum.MakeAccum(Math.Max(Math.Min(n.Value, max.Value), min.Value)));
}
/// <summary>
/// Clamps a number between a minimum and a maximum.
/// </summary>
/// <param name="n">The number to clamp.</param>
/// <param name="min">The minimum allowed value.</param>
/// <param name="max">The maximum allowed value.</param>
/// <returns>min, if n is lower than min; max, if n is higher than max; n otherwise.</returns>
public static Accum ClampInt(Accum n, int min, int max)
{
return(Accum.MakeAccum(Math.Max(Math.Min(n.Value, max << 16), min << 16)));
}
/// <summary>
/// Convert radians to degrees.
/// </summary>
/// <param name="radians">An angle in radians.</param>
/// <returns>The angle expressed in degrees.</returns>
public static Accum RadiansToDegrees(Accum radians)
{
return(radians * radToDegAccum);
}
/// <summary>
/// Convert degrees to radians.
/// </summary>
/// <param name="degrees">An angle in degrees.</param>
/// <returns>The angle expressed in radians.</returns>
public static Accum DegreesToRadians(Accum degrees)
{
return(degrees * degToRadAccum);
}
public static Accum Cos(Accum x)
{
return(Sin(x + PIOver2));
}
public Vertex(Accum x, Accum y, Accum z, Accum normal) :
this(x, y, z)
{
Normal = normal;
}
public static bool IsBetween(Accum x, Accum min, Accum max)
{
return(x >= min && x <= max);
}
public Vertex(Accum x, Accum y, Accum z)
{
X = x;
Y = y;
Z = z;
}