/// <summary>
/// Creates a quaternion from an axis and an angle (in radians).
/// </summary>
public static hquat FromAxisAngle(Half angle, hvec3 v)
{
var s = Math.Sin((double)angle * 0.5);
var c = Math.Cos((double)angle * 0.5);
return(new hquat((Half)((double)v.x * s), (Half)((double)v.y * s), (Half)((double)v.z * s), (Half)c));
}
public void Constructors()
{
{
var v = new hvec3(new Half(-3.5));
Assert.AreEqual(new Half(-3.5), v.x);
Assert.AreEqual(new Half(-3.5), v.y);
Assert.AreEqual(new Half(-3.5), v.z);
}
{
var v = new hvec3(new Half(-4.5), new Half(8), new Half(-6.5));
Assert.AreEqual(new Half(-4.5), v.x);
Assert.AreEqual(new Half(8), v.y);
Assert.AreEqual(new Half(-6.5), v.z);
}
{
var v = new hvec3(new hvec2(new Half(7), new Half(9.5)));
Assert.AreEqual(new Half(7), v.x);
Assert.AreEqual(new Half(9.5), v.y);
Assert.AreEqual(Half.Zero, v.z);
}
{
var v = new hvec3(new hvec3(new Half(-3.5), new Half(-5.5), new Half(2)));
Assert.AreEqual(new Half(-3.5), v.x);
Assert.AreEqual(new Half(-5.5), v.y);
Assert.AreEqual(new Half(2), v.z);
}
{
var v = new hvec3(new hvec4(new Half(-2.5), new Half(3.5), new Half(-4.5), new Half(-0.5)));
Assert.AreEqual(new Half(-2.5), v.x);
Assert.AreEqual(new Half(3.5), v.y);
Assert.AreEqual(new Half(-4.5), v.z);
}
}
/// <summary>
/// vector-and-scalar constructor (CAUTION: not angle-axis, use FromAngleAxis instead)
/// </summary>
public hquat(hvec3 v, Half s)
{
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = s;
}
/// <summary>
/// Returns a vector rotated by the quaternion.
/// </summary>
public static hvec3 operator*(hquat q, hvec3 v)
{
var qv = new hvec3(q.x, q.y, q.z);
var uv = hvec3.Cross(qv, v);
var uuv = hvec3.Cross(qv, uv);
return(v + ((uv * q.w) + uuv) * 2);
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat2x3(hvec3 c0, hvec3 c1)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
}
/// <summary>
/// Create a quaternion from two normalized axis (http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors)
/// </summary>
public hquat(hvec3 eulerAngle)
{
var c = hvec3.Cos(eulerAngle / 2);
var s = hvec3.Sin(eulerAngle / 2);
this.x = s.x * c.y * c.z - c.x * s.y * s.z;
this.y = c.x * s.y * c.z + s.x * c.y * s.z;
this.z = c.x * c.y * s.z - s.x * s.y * c.z;
this.w = c.x * c.y * c.z + s.x * s.y * s.z;
}
public void PropertyValues()
{
var v = new hvec3(new Half(-2), new Half(7), new Half(-5.5));
var vals = v.Values;
Assert.AreEqual(new Half(-2), vals[0]);
Assert.AreEqual(new Half(7), vals[1]);
Assert.AreEqual(new Half(-5.5), vals[2]);
Assert.That(vals.SequenceEqual(v.ToArray()));
}
/// <summary>
/// Create a quaternion from two normalized axis (http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors)
/// </summary>
public hquat(hvec3 u, hvec3 v)
{
var localW = hvec3.Cross(u, v);
var dot = hvec3.Dot(u, v);
var q = new hquat(localW.x, localW.y, localW.z, Half.One + dot).Normalized;
this.x = q.x;
this.y = q.y;
this.z = q.z;
this.w = q.w;
}
public void SerializationJson()
{
var v0 = new hvec3(new Half(-2), new Half(-4), new Half(3));
var s0 = JsonConvert.SerializeObject(v0);
var v1 = JsonConvert.DeserializeObject <hvec3>(s0);
var s1 = JsonConvert.SerializeObject(v1);
Assert.AreEqual(v0, v1);
Assert.AreEqual(s0, s1);
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat2x4(hvec3 c0, hvec3 c1)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m03 = Half.Zero;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m13 = Half.Zero;
}
public void InvariantCrossDot()
{
{
var v0 = new hvec3(new Half(-8.5), new Half(3), Half.Zero);
var v1 = new hvec3(new Half(3.5), new Half(-4), new Half(9.5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(-3.5), new Half(7), new Half(0.5));
var v1 = new hvec3(new Half(7), new Half(8.5), new Half(2));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(4.5), new Half(-8), new Half(3));
var v1 = new hvec3(new Half(-1.5), new Half(1.5), new Half(-6.5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(Half.Zero, new Half(-9), new Half(2.5));
var v1 = new hvec3(new Half(-6), new Half(3.5), new Half(8.5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(8), new Half(4), new Half(8));
var v1 = new hvec3(new Half(-5.5), new Half(8.5), new Half(0.5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(-1), new Half(-3), new Half(1.5));
var v1 = new hvec3(new Half(9), new Half(2.5), new Half(-7));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(-3), new Half(-6.5), new Half(-4.5));
var v1 = new hvec3(new Half(-9.5), new Half(2.5), new Half(9.5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(-4), new Half(3.5), new Half(9.5));
var v1 = new hvec3(new Half(-3.5), new Half(6.5), Half.One);
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(-7), new Half(7.5), new Half(-5));
var v1 = new hvec3(new Half(7), new Half(-4), new Half(-5));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
{
var v0 = new hvec3(new Half(8), new Half(5), new Half(-1));
var v1 = new hvec3(Half.One, new Half(-4.5), new Half(8));
Assert.Less(glm.Abs(glm.Dot(v0, glm.Cross(v0, v1))), 0.1);
}
}
public void TriangleInequality()
{
{
var v0 = new hvec3(new Half(0.5), new Half(-8.5), Half.Zero);
var v1 = new hvec3(new Half(-6.5), new Half(4), new Half(-3.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(9.5), Half.One, new Half(3.5));
var v1 = new hvec3(new Half(-8.5), Half.Zero, new Half(-6.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(-9.5), Half.One, new Half(-8));
var v1 = new hvec3(new Half(-5.5), new Half(3), new Half(-6.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(1.5), new Half(4), new Half(-1.5));
var v1 = new hvec3(new Half(6.5), new Half(8.5), new Half(-5.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(-9), new Half(-6.5), Half.One);
var v1 = new hvec3(new Half(-5), new Half(9.5), new Half(-8.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(-2.5), new Half(7.5), new Half(4));
var v1 = new hvec3(new Half(4.5), new Half(-9), new Half(-3));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(-8.5), new Half(-2.5), new Half(3.5));
var v1 = new hvec3(new Half(-8.5), new Half(2), new Half(-9));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(5), new Half(2), new Half(8.5));
var v1 = new hvec3(new Half(3.5), new Half(6.5), new Half(-3));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(9.5), new Half(-3.5), new Half(2.5));
var v1 = new hvec3(new Half(-6.5), new Half(-5.5), new Half(-3));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
{
var v0 = new hvec3(new Half(-7), new Half(3.5), new Half(-6.5));
var v1 = new hvec3(new Half(-6), new Half(3), new Half(-7.5));
Assert.GreaterOrEqual(v0.NormMax + v1.NormMax, (v0 + v1).NormMax);
}
}
public void InvariantCommutativeNeg()
{
{
var v0 = new hvec3(new Half(9.5), new Half(3), new Half(5));
var v1 = new hvec3(new Half(-9), new Half(9.5), new Half(2));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(0.5), new Half(5), new Half(3.5));
var v1 = new hvec3(new Half(-3.5), new Half(8), new Half(3.5));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(-8), new Half(2), new Half(7));
var v1 = new hvec3(new Half(-7), new Half(9.5), Half.Zero);
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(8.5), new Half(8), new Half(5.5));
var v1 = new hvec3(new Half(-5.5), new Half(-0.5), new Half(1.5));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(-2.5), new Half(-7), new Half(6));
var v1 = new hvec3(new Half(3.5), new Half(-7.5), new Half(-2));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(9.5), new Half(-7.5), new Half(-2));
var v1 = new hvec3(new Half(6.5), new Half(-5), new Half(-9.5));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(5.5), new Half(-4.5), new Half(-7.5));
var v1 = new hvec3(new Half(-7), new Half(-6.5), new Half(4.5));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(new Half(-2.5), new Half(0.5), new Half(-5));
var v1 = new hvec3(new Half(-3.5), new Half(9), new Half(-8));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(Half.Zero, new Half(9.5), Half.Zero);
var v1 = new hvec3(new Half(-8.5), new Half(-7.5), new Half(-4));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
{
var v0 = new hvec3(Half.Zero, new Half(-6), new Half(-5));
var v1 = new hvec3(new Half(-4), new Half(1.5), new Half(-7.5));
Assert.AreEqual(v0 - v1, -(v1 - v0));
}
}
public void InvariantCommutative()
{
{
var v0 = new hvec3(new Half(8), new Half(5), new Half(-6));
var v1 = new hvec3(new Half(-2.5), new Half(-3), new Half(0.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-5.5), new Half(-1.5), new Half(-6.5));
var v1 = new hvec3(new Half(6), new Half(-8.5), new Half(-0.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(0.5), new Half(6.5), new Half(0.5));
var v1 = new hvec3(new Half(0.5), new Half(3), new Half(-4.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-2), new Half(-3), new Half(5));
var v1 = new hvec3(new Half(9.5), new Half(2), new Half(-8.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(3.5), new Half(8), new Half(8));
var v1 = new hvec3(new Half(-3.5), new Half(-7), new Half(6));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-3), new Half(-9), new Half(7.5));
var v1 = new hvec3(new Half(7.5), new Half(-8), new Half(-8));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(9), new Half(-2), new Half(2.5));
var v1 = new hvec3(new Half(-9.5), new Half(6), new Half(-9.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-1.5), new Half(0.5), new Half(1.5));
var v1 = new hvec3(new Half(3.5), new Half(9.5), new Half(7.5));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-0.5), new Half(-3), new Half(-4.5));
var v1 = new hvec3(new Half(8), new Half(-4), new Half(6));
Assert.AreEqual(v0 * v1, v1 * v0);
}
{
var v0 = new hvec3(new Half(-8), new Half(9), new Half(2));
var v1 = new hvec3(new Half(4.5), new Half(4.5), new Half(4));
Assert.AreEqual(v0 * v1, v1 * v0);
}
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat3(hvec3 c0, hvec3 c1, hvec3 c2)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m20 = c2.x;
this.m21 = c2.y;
this.m22 = c2.z;
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat3(hvec3 c0, hvec3 c1)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m20 = Half.Zero;
this.m21 = Half.Zero;
this.m22 = Half.One;
}
public void Operators()
{
var v1 = new hvec3(new Half(-4.5), new Half(-4.5), new Half(7.5));
var v2 = new hvec3(new Half(-4.5), new Half(-4.5), new Half(7.5));
var v3 = new hvec3(new Half(7.5), new Half(-4.5), new Half(-4.5));
Assert.That(v1 == new hvec3(v1));
Assert.That(v2 == new hvec3(v2));
Assert.That(v3 == new hvec3(v3));
Assert.That(v1 == v2);
Assert.That(v1 != v3);
Assert.That(v2 != v3);
}
public void StringInterop()
{
var v = new hvec3(new Half(7), new Half(-3), new Half(3));
var s0 = v.ToString();
var s1 = v.ToString("#");
var v0 = hvec3.Parse(s0);
var v1 = hvec3.Parse(s1, "#");
Assert.AreEqual(v, v0);
Assert.AreEqual(v, v1);
var b0 = hvec3.TryParse(s0, out v0);
var b1 = hvec3.TryParse(s1, "#", out v1);
Assert.That(b0);
Assert.That(b1);
Assert.AreEqual(v, v0);
Assert.AreEqual(v, v1);
b0 = hvec3.TryParse(null, out v0);
Assert.False(b0);
b0 = hvec3.TryParse("", out v0);
Assert.False(b0);
b0 = hvec3.TryParse(s0 + ", 0", out v0);
Assert.False(b0);
Assert.Throws <NullReferenceException>(() => { hvec3.Parse(null); });
Assert.Throws <FormatException>(() => { hvec3.Parse(""); });
Assert.Throws <FormatException>(() => { hvec3.Parse(s0 + ", 0"); });
var s2 = v.ToString(";", CultureInfo.InvariantCulture);
Assert.That(s2.Length > 0);
var s3 = v.ToString("; ", "G");
var s4 = v.ToString("; ", "G", CultureInfo.InvariantCulture);
var v3 = hvec3.Parse(s3, "; ", NumberStyles.Number);
var v4 = hvec3.Parse(s4, "; ", NumberStyles.Number, CultureInfo.InvariantCulture);
Assert.AreEqual(v, v3);
Assert.AreEqual(v, v4);
var b4 = hvec3.TryParse(s4, "; ", NumberStyles.Number, CultureInfo.InvariantCulture, out v4);
Assert.That(b4);
Assert.AreEqual(v, v4);
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat3x4(hvec3 c0, hvec3 c1, hvec3 c2)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m03 = Half.Zero;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m13 = Half.Zero;
this.m20 = c2.x;
this.m21 = c2.y;
this.m22 = c2.z;
this.m23 = Half.Zero;
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat4x3(hvec3 c0, hvec3 c1, hvec3 c2, hvec3 c3)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m20 = c2.x;
this.m21 = c2.y;
this.m22 = c2.z;
this.m30 = c3.x;
this.m31 = c3.y;
this.m32 = c3.z;
}
/// <summary>
/// Constructs this matrix from a series of column vectors. Non-overwritten fields are from an Identity matrix.
/// </summary>
public hmat4x3(hvec3 c0, hvec3 c1, hvec3 c2)
{
this.m00 = c0.x;
this.m01 = c0.y;
this.m02 = c0.z;
this.m10 = c1.x;
this.m11 = c1.y;
this.m12 = c1.z;
this.m20 = c2.x;
this.m21 = c2.y;
this.m22 = c2.z;
this.m30 = Half.Zero;
this.m31 = Half.Zero;
this.m32 = Half.Zero;
}
public void HalfSerializationJson()
{
var h = new Half(2.2);
var sh = JsonConvert.SerializeObject(h);
Console.WriteLine(sh);
var v0 = new hvec3(new Half(-2), new Half(-4), new Half(3));
var s0 = JsonConvert.SerializeObject(v0);
var v1 = JsonConvert.DeserializeObject <hvec3>(s0);
var s1 = JsonConvert.SerializeObject(v1);
Assert.AreEqual(v0, v1);
Assert.AreEqual(s0, s1);
}
public void InvariantId()
{
{
var v0 = new hvec3(new Half(8), new Half(8), Half.One);
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(-4), new Half(-4.5), new Half(2));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(7), new Half(6), new Half(0.5));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(7), new Half(-7.5), new Half(9));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(-9), new Half(2), new Half(-5));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(9.5), Half.One, new Half(1.5));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(-7), new Half(3), new Half(-6.5));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(-5.5), new Half(8.5), Half.One);
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(new Half(-7.5), new Half(-3), new Half(-9));
Assert.AreEqual(v0, +v0);
}
{
var v0 = new hvec3(Half.One, new Half(2.5), new Half(8.5));
Assert.AreEqual(v0, +v0);
}
}
public void InvariantDouble()
{
{
var v0 = new hvec3(new Half(-5.5), new Half(-9.5), new Half(9.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(7), new Half(7.5), new Half(5.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(2), new Half(5.5), new Half(-7.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(0.5), new Half(-2), new Half(-2.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(8), new Half(8), new Half(7));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(2.5), new Half(-1.5), new Half(-1.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(8.5), new Half(6.5), new Half(-3.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(6), new Half(-7), new Half(-4));
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(7), new Half(-8.5), Half.Zero);
Assert.AreEqual(v0 + v0, 2 * v0);
}
{
var v0 = new hvec3(new Half(4.5), new Half(6.5), new Half(7.5));
Assert.AreEqual(v0 + v0, 2 * v0);
}
}
public void InvariantTriple()
{
{
var v0 = new hvec3(new Half(-8), new Half(4), Half.One);
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(-7), new Half(4.5), new Half(-2));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(-8.5), new Half(-8.5), new Half(2));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(-2), new Half(-4), new Half(-7));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(2.5), new Half(-5), new Half(3.5));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(4), new Half(9.5), new Half(-5));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(-4), new Half(4), new Half(-9));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(3), new Half(-8), new Half(4.5));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(5), new Half(-6.5), new Half(-5.5));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
{
var v0 = new hvec3(new Half(3), new Half(3), new Half(8));
Assert.AreEqual(v0 + v0 + v0, 3 * v0);
}
}
public void InvariantIdNeg()
{
{
var v0 = new hvec3(new Half(4.5), new Half(-9.5), new Half(-0.5));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(-3), new Half(-7.5), Half.Zero);
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(6.5), new Half(5.5), new Half(4));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(2), new Half(-7.5), new Half(5.5));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(Half.Zero, new Half(7.5), new Half(-0.5));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(Half.One, new Half(0.5), new Half(-4.5));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(-7.5), new Half(9.5), new Half(5.5));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(5), new Half(6.5), new Half(-7));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(8), new Half(-2), new Half(4));
Assert.AreEqual(v0, -(-v0));
}
{
var v0 = new hvec3(new Half(4.5), Half.Zero, new Half(-1));
Assert.AreEqual(v0, -(-v0));
}
}
public void InvariantNorm()
{
{
var v0 = new hvec3(new Half(-8.5), new Half(-6), new Half(-7));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-7), new Half(-5), new Half(3.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(4), new Half(-7), new Half(4.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-5), new Half(-1.5), new Half(5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(Half.One, new Half(8.5), new Half(9.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(3.5), new Half(3), new Half(-3.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-1.5), new Half(-7.5), new Half(0.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-2), new Half(5), new Half(-8.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-8.5), new Half(-3.5), new Half(-3));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
{
var v0 = new hvec3(new Half(-8.5), new Half(8), new Half(-0.5));
Assert.LessOrEqual(v0.NormMax, v0.Norm);
}
}
/// <summary> /// Rotates this quaternion from an axis and an angle (in radians). /// </summary> public static hquat Rotated(hquat q, Half angle, hvec3 v) => q.Rotated(angle, v);
/// <summary> /// Rotates this quaternion from an axis and an angle (in radians). /// </summary> public hquat Rotated(Half angle, hvec3 v) => this * FromAxisAngle(angle, v);
/// <summary> /// OuterProduct treats the first parameter c as a column vector (matrix with one column) and the second parameter r as a row vector (matrix with one row) and does a linear algebraic matrix multiply c * r, yielding a matrix whose number of rows is the number of components in c and whose number of columns is the number of components in r. /// </summary> public static hmat3x4 OuterProduct(hvec4 c, hvec3 r) => hvec4.OuterProduct(c, r);
