public static Quaternion CalcBodyToImuRotationFromPitch(Quaternion q1, Quaternion q2, bool snapToGrid = true)
{
// move to GlmSharp structs
quat _q1 = new quat((float)q1.X, (float)q1.Y, (float)q1.Z, (float)q1.W);
quat _q2 = new quat((float)q2.X, (float)q2.Y, (float)q2.Z, (float)q2.W);
// normalize input quaternions
_q1 = _q1.Normalized;
_q2 = _q2.Normalized;
// find rotation from Body frame to the Inertial frame
quat q_axis = _q1 * _q2.Inverse;
vec3 y_bi = q_axis.Axis;
if (snapToGrid)
{
y_bi[2] = 0.0f;
}
y_bi = y_bi.Normalized;
vec3 z_bi = new vec3(0.0f, 0.0f, 1.0f);
vec3 x_bi = vec3.Cross(y_bi, z_bi).Normalized;
mat3 R_ib = new mat3(x_bi, y_bi, z_bi);
quat q_bi = R_ib.Transposed.ToQuaternion;
// calculate the (fixed) rotation from the IMU frame to the Body frame
quat q_bm = (q_bi * _q1).Inverse.Normalized;
return(new Quaternion(q_bm.x, q_bm.y, q_bm.z, q_bm.w));
}
public static int Main(string[] args)
{
mat2 m = (1, 2, 0, -1);
poly p1 = (0, 0, 0, 2);
poly p2 = (0, 0, 3);
var r0 = p2.Derivative;
var r1 = p1 << 1;
var r2 = p1 >> 1;
var r3 = p1 + p2;
var r4 = p1 - p2;
var r5 = p1 * p2;
var r6 = p1 / p2;
var r7 = p1 % p2;
mat3 mat = (
1, 1, 1,
1, 0, 1,
1, 0, 1
);
vec3 b = (0, 4, 2);
var x = mat.Solve(b);
poly p3 = (-1, 1);
poly p4 = (-1, 0, 1);
poly p5 = (-1, 0, 0, 1);
poly p6 = (0, 0, 0, 0, 0, 0, 1);
poly p7 = (2, 1, 8, 3);
return(0);
}
/// <summary>
/// </summary>
/// <param name="uniformName"></param>
/// <param name="matrixes"></param>
internal int glUniform(string uniformName, mat3[] matrixes)
{
int location = GetUniformLocation(uniformName);
if (location >= 0)
{
if (glUniformMatrix3fv == null)
{
glUniformMatrix3fv = GL.Instance.GetDelegateFor("glUniformMatrix3fv", GLDelegates.typeof_void_int_int_bool_floatN) as GLDelegates.void_int_int_bool_floatN;
}
var values = new float[matrixes.Length * 9];
for (int index = 0, i = 0; i < matrixes.Length; i++)
{
mat3 matrix = matrixes[i];
values[index++] = matrix.col0.x;
values[index++] = matrix.col0.y;
values[index++] = matrix.col0.z;
values[index++] = matrix.col1.x;
values[index++] = matrix.col1.y;
values[index++] = matrix.col1.z;
values[index++] = matrix.col2.x;
values[index++] = matrix.col2.y;
values[index++] = matrix.col2.z;
}
glUniformMatrix3fv(location, matrixes.Length, false, values);
}
return(location);
}
/// <summary>
/// This test shows that glm.rotate() and Quaternion.ToRotationMatrix() give the same result.
/// </summary>
public static void Test()
{
using (var writer = new StreamWriter("test-quaternion.txt"))
{
int length = 5;
for (int angleDegree = 1; angleDegree < 361; angleDegree++)
{
for (int x = -length; x < length; x++)
{
for (int y = -length; y < length; y++)
{
for (int z = -length; z < length; z++)
{
var quaternion = new Quaternion(angleDegree, new vec3(x, y, z));
mat3 matrix1 = quaternion.ToRotationMatrix();
//mat4 tmp = glm.rotate((float)(angleDegree * Math.PI / 180.0f), new vec3(x, y, z));
mat4 tmp = glm.rotate(angleDegree, new vec3(x, y, z));
mat3 matrix2 = tmp.to_mat3();
writer.WriteLine("====================");
writer.WriteLine("{3}° x[{0}] y[{1}] z[{2}]", x, y, z, angleDegree);
writer.WriteLine(matrix1.ToArray().PrintVectors(3, ",", ";" + Environment.NewLine));
writer.WriteLine("------------");
writer.WriteLine(matrix2.ToArray().PrintVectors(3, ",", ";" + Environment.NewLine));
//}
}
}
}
}
writer.WriteLine("Test finished.");
}
}
/// <summary>
/// 把连续9个float值按照列优先的顺序转换为mat3
/// </summary>
/// <param name="values"></param>
/// <param name="startIndex"></param>
/// <returns></returns>
public static mat3 ToMat3(this float[] values, int startIndex = 0)
{
mat3 result = new mat3(
values.ToVec3(startIndex + 0), values.ToVec3(startIndex + 3), values.ToVec3(startIndex + 6));
return result;
}
public void CheckMatrixReferenceEquality()
{
vec2 v2_1 = new vec2(1, 0);
vec2 v2_2 = new vec2(1, 0);
vec2 v2_3 = new vec2(0, 0);
mat2 m2_1 = new mat2(v2_1, v2_2);
mat2 m2_2 = new mat2(v2_1, v2_2);
mat2 m2_3 = new mat2(v2_1, v2_3);
vec3 v3_1 = new vec3(1, 0, 1);
vec3 v3_2 = new vec3(1, 0, 1);
vec3 v3_3 = new vec3(0, 0, 1);
mat3 m3_1 = new mat3(v3_1, v3_2, v3_2);
mat3 m3_2 = new mat3(v3_1, v3_2, v3_2);
mat3 m3_3 = new mat3(v3_1, v3_2, v3_3);
vec4 v4_1 = new vec4(1, 0, 1, 1);
vec4 v4_2 = new vec4(1, 0, 1, 1);
vec4 v4_3 = new vec4(0, 0, 1, 1);
mat4 m4_1 = new mat4(v4_1, v4_2, v4_2, v4_2);
mat4 m4_2 = new mat4(v4_1, v4_2, v4_2, v4_2);
mat4 m4_3 = new mat4(v4_1, v4_2, v4_2, v4_3);
Assert.AreEqual(m2_1.GetHashCode(), m2_2.GetHashCode(), "Error Hashcodes are not the Same");
Assert.AreNotEqual(m2_1.GetHashCode(), m2_3.GetHashCode(), "Error Hashcodes are the Same");
Assert.AreEqual(m3_1.GetHashCode(), m3_2.GetHashCode(), "Error Hashcodes are not the Same");
Assert.AreNotEqual(m3_1.GetHashCode(), m3_3.GetHashCode(), "Error Hashcodes are the Same");
Assert.AreEqual(m4_1.GetHashCode(), m4_2.GetHashCode(), "Error Hashcodes are not the Same");
Assert.AreNotEqual(m4_1.GetHashCode(), m4_3.GetHashCode(), "Error Hashcodes are the Same");
}
/// <summary>
/// Calculates the rotation matrix around a given axis with a angle in degree
/// </summary>
/// <param name="rotationAxis"></param>
/// <param name="angle"></param>
/// <returns></returns>
public static mat3 calculateRotationMatrix(vec4 rotationAxis, float angle)
{
mat3 m = new mat3(1);
float s = glm.sin(glm.radians(angle));
s = (Math.Abs(s) < Constants.Epsilon) ? 0 : s;
float c = glm.cos(glm.radians(angle));
c = (Math.Abs(c) < Constants.Epsilon) ? 0 : c;
float t = 1 - glm.cos(glm.radians(angle));
t = (Math.Abs(t) < Constants.Epsilon) ? 0 : t;
float x = rotationAxis[0];
float y = rotationAxis[1];
float z = rotationAxis[2];
m[0, 0] = t * x * x + c;
m[0, 1] = t * x * y + s * z;
m[0, 2] = t * x * z - s * y;
m[1, 0] = t * x * y - s * z;
m[1, 1] = t * y * y + c;
m[1, 2] = t * z * y + x * s;
m[2, 0] = t * x * z + s * y;
m[2, 1] = t * y * z - s * x;
m[2, 2] = t * z * z + c;
return(m);
}
public void OnCreate(ECSWorld world)
{
var fragShader = Asset.Load <ShaderAsset>("mesh_instanced_default.frag");
var vertShader = Asset.Load <ShaderAsset>("mesh_instanced_default.vert");
var shader = new ShaderPipeline(fragShader, vertShader, ShaderType.Instanced);
defaultShader = shader.ShaderPair;
defaultMaterial = new Material(GraphicsContext.graphicsDevice,
GraphicsContext.uniform0, defaultShader);
defaultMaterial.wireframe = true;
instanceMatrix = new DeviceBuffer(GraphicsContext.graphicsDevice, (ulong)Unsafe.SizeOf <ObjectToWorld>(),
BufferUsageFlags.VertexBuffer, BufferMemoryUsageHint.Dynamic);
var matrix = mat4.Identity;
var normalMatrix = new mat3(matrix);
ObjectToWorld matrices = new ObjectToWorld()
{
model = matrix,
normal = normalMatrix
};
instanceMatrix.SetData(matrices, 0);
MeshData initialData = new MeshData();
initialData.subMeshes = new SubMeshData[1];
initialData.subMeshes[0] = new SubMeshData(vertices, indices);
defaultMesh = new Mesh(GraphicsContext.graphicsDevice, initialData, true);
}
/// <summary>
/// </summary>
public static void Test2()
{
using (var writer = new StreamWriter("test-quaternion2.txt"))
{
int length = 5;
for (int angleDegree = 1; angleDegree < 361; angleDegree++)
{
for (int x = -length; x < length; x++)
{
for (int y = -length; y < length; y++)
{
for (int z = -length; z < length; z++)
{
var quaternion = new Quaternion(angleDegree, new vec3(x, y, z));
mat3 matrix1 = quaternion.ToRotationMatrix();
Quaternion quaternion2 = matrix1.ToQuaternion();
writer.WriteLine("====================");
writer.WriteLine("{3}° x[{0}] y[{1}] z[{2}]", x, y, z, angleDegree);
writer.WriteLine(quaternion);
writer.WriteLine("------------");
writer.WriteLine(quaternion2);
//}
}
}
}
}
writer.WriteLine("Test finished.");
}
}
/*
* 3x3 matrix determinant
*/
private double det3(mat3 m)
{
double res = m.matrix[0, 0] * (m.matrix[1, 1] * m.matrix[2, 2] - m.matrix[1, 2] * m.matrix[2, 1])
- m.matrix[0, 1] * (m.matrix[1, 0] * m.matrix[2, 2] - m.matrix[1, 2] * m.matrix[2, 0])
+ m.matrix[0, 2] * (m.matrix[1, 0] * m.matrix[2, 1] - m.matrix[1, 1] * m.matrix[2, 0]);
return(res);
}
public override void UpdatePos(vec2 pos)
{
base.UpdatePos(pos);
float r = R;
_translate = Transforms.Translate(pos.x, pos.y);
VertexStrPos = new vec2(VertexStr.Length == 1 ? pos.x - r / 2f + 2f : pos.x - r + 6f, pos.y - r / 2f);
Lines = _circle.Lines.Select(p => (vec2)(_translate * p)).ToArray();
}
/// <summary>
/// Applies a scale transformation to matrix <paramref name="m"/> by vector <paramref name="v"/>.
/// </summary>
/// <param name="m">The matrix to transform.</param>
/// <param name="v">The vector to scale by.</param>
/// <returns><paramref name="m"/> scaled by <paramref name="v"/>.</returns>
public static mat3 scale(mat3 m, vec2 v)
{
mat3 result = m;
result.col0 = m.col0 * v.x;
result.col1 = m.col1 * v.y;
result.col2 = m.col2;
return result;
}
internal override void SetValue(ValueType value)
{
if (value.GetType() != typeof(mat3))
{
throw new ArgumentException(string.Format("[{0}] not match [{1}]'s value.",
value.GetType().Name, this.GetType().Name));
}
this.Value = (mat3)value;
}
private static void rotateXalignment()
{
mat3 _rotationMatrix = Calculation.calculateRotationMatrix(cubeXaxis, cubeRotationAngle);
mat4 _transformation = Calculation.calculateTransformationMatrix(new vec4(0), _rotationMatrix, new vec3(1));
foreach (var _o in groupXalignmentLeft)
{
_o.updateObject(_transformation);
}
}
/// <summary>
/// Creates the modelview and normal matrix. Also rotates the sceen by a specified amount.
/// </summary>
/// <param name="rotationAngle">The rotation angle, in radians.</param>
public void CreateModelviewAndNormalMatrix(float rotationAngle)
{
// Create the modelview and normal matrix. We'll also rotate the scene
// by the provided rotation angle, which means things that draw it
// can make the scene rotate easily.
mat4 rotation = glm.rotate(mat4.identity(), rotationAngle, new vec3(0, 1, 0));
mat4 translation = glm.translate(mat4.identity(), new vec3(0, 0, -4));
modelviewMatrix = rotation * translation;
normalMatrix = modelviewMatrix.to_mat3();
}
public override void SetDeclarations(ref ShaderVariables shaderVars)
{
Matrix3 rot = new Matrix3();
rot.MakeFromRPY(_Rotation.x, _Rotation.y, _Rotation.z);
mat3 glRot = rot.GetGLMat3();
shaderVars.Add("fracScale" + _Iteration, _Scale);
shaderVars.Add("fracRot" + _Iteration, glRot);
shaderVars.Add("fracMinRad" + _Iteration, (float)_MinRadius);
}
public GenObject(string name)
{
IsSelectable = true;
IsVisible = true;
IsRenderable = true;
Name = name;
IsSelected = false;
TransformationMatrix = new mat4(1.0f);
NormalTransformMatrix = new mat3(1.0f);
}
vec3 PerturbNormal(vec3 N, vec3 V, vec2 texcoord)
{
// N, la normale interpolée et
// V, le vecteur vue (vertex dirigé vers l'œil)
vec3 map = texture(materialState.textureNormal, texcoord).rgb;
map = map * 255f / 127f - 128f / 127f;
mat3 TBN = CotangentFrame(N, -V, texcoord);
return(normalize(TBN * map));
}
public void Set(string name, mat3 val, bool transpose = false, bool keep_layout = true)
{
if (Values.TryGetValue(name, out var v))
{
v.Set(val, transpose, keep_layout);
}
else
{
Values.Add(name, new Value(val, transpose)); Keys.AddLast(name);
}
}
/// <summary>
/// Gets the transposed matrix.
/// <para>获取转置矩阵。</para>
/// </summary>
/// <param name="m"></param>
/// <returns></returns>
public static mat3 transpose(mat3 m)
{
vec3 col0 = m.col0;
vec3 col1 = m.col1;
vec3 col2 = m.col2;
return(new mat3(
new vec3(col0.x, col1.x, col2.x),
new vec3(col0.y, col1.y, col2.y),
new vec3(col0.z, col1.z, col2.z)
));
}
public DebuggerProxy(mat3 m)
{
m00 = m.m00;
m01 = m.m01;
m02 = m.m02;
m10 = m.m10;
m11 = m.m11;
m12 = m.m12;
m20 = m.m20;
m21 = m.m21;
m22 = m.m22;
}
private void UpdateInertia()
{
var t = Parent.Transform;
t.Translation = vec3.Zero;
var worldspaceMat = new mat3()
{
Row0 = t * vec3.UnitX, Row1 = t * vec3.UnitY, Row2 = t * vec3.UnitZ
};
InverseInertiaWorldspace = worldspaceMat.Transposed * InverseInertia * worldspaceMat;
}
public static float[] serialize(this mat3 value, float[] array = null)
{
array = array ?? new float[9];
if (array.Length != 9)
{
throw new ArgumentException("Invalid array length.");
}
for (var c = 0; c < 9; ++c)
{
array[c] = value[c / 3, c % 3];
}
return(array);
}
public static mat3 Transpose(ref mat3 m)
{
mat3 trans = new mat3(1.0f);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
trans[j, i] = m[i, j];
}
}
return(trans);
}
public void DetermineAdjugateComponents(double[] a, double[] result)
{
var matA = new mat3(a);
var expected = new mat3(result);
for (int r = 0; r < 3; r++)
{
for (int c = 0; c < 3; c++)
{
matA.AdjugateComponent(r, c).Should().BeApproximately(expected[r, c], double.Epsilon);
}
}
}
/// Builds a rotation 3 * 3 matrix created from an angle.
/// </summary>
/// <param name="m">The m.</param>
/// <param name="angleDegree">ANgle in Degree.</param>
/// <returns></returns>
public static mat3 rotate(mat3 m, float angleDegree)
{
float c = (float)Math.Cos(angleDegree * Math.PI / 180.0);
float s = (float)Math.Sin(angleDegree * Math.PI / 180.0);
mat3 rotate = mat3.identity();
rotate.col0 = new vec2(c, s);
rotate.col1 = new vec2(-s, c);
mat3 result = rotate * m;
return result;
}
public static unsafe void glusRaytraceLookAtf(this float[] positionBuffer, float[] directionBuffer, float[] originDirectionBuffer, byte padding, int width, int height, float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ)
{
//float forward[3], side[3], up[3];
//float rotation[9];
vec3 forward, side, up;
float[] rotation;
int i, k;
forward = new vec3(centerX - eyeX, centerY - eyeY, centerZ - eyeZ);
forward = forward.normalize();
up = new vec3(upX, upY, upZ);
side = forward.cross(up);
side = side.normalize();
up = side.cross(forward);
mat3 matrix = new mat3(side, up, -forward);
rotation = matrix.ToArray();
for (i = 0; i < width * height; i++)
{
positionBuffer[i * 4 + 0] = eyeX;
positionBuffer[i * 4 + 1] = eyeY;
positionBuffer[i * 4 + 2] = eyeZ;
positionBuffer[i * 4 + 3] = 1.0f;
//glusMatrix3x3MultiplyVector3f(&directionBuffer[i * (3 + padding)], rotation, &originDirectionBuffer[i * (3 + padding)]);
float[] result = new float[3];
result[0] = directionBuffer[i * (3 + padding) + 0];
result[1] = directionBuffer[i * (3 + padding) + 1];
result[2] = directionBuffer[i * (3 + padding) + 2];
float[] vector = new float[3];
vector[0] = originDirectionBuffer[i * (3 + padding) + 0];
vector[1] = originDirectionBuffer[i * (3 + padding) + 1];
vector[2] = originDirectionBuffer[i * (3 + padding) + 2];
glusMatrix3x3MultiplyVector3f(result, rotation, vector);
directionBuffer[i * (3 + padding) + 0] = result[0];
directionBuffer[i * (3 + padding) + 1] = result[1];
directionBuffer[i * (3 + padding) + 2] = result[2];
for (k = 0; k < padding; k++)
{
directionBuffer[i * (3 + padding) + 3 + k] = originDirectionBuffer[i * (3 + padding) + 3 + k];
}
}
}
/// <summary>
/// </summary>
/// <param name="uniformName"></param>
/// <param name="m"></param>
public int glUniform(string uniformName, mat3 m)
{
int location = GetUniformLocation(uniformName);
if (location >= 0)
{
if (glUniformMatrix3fv == null)
{
glUniformMatrix3fv = OpenGL.GetDelegateFor <OpenGL.glUniformMatrix3fv>();
}
float[] array = m.ToArray();
glUniformMatrix3fv(location, 1, false, array);
}
return(location);
}
public mat3 GetGLMat3()
{
mat3 ret = new mat3(1);
ret[0, 0] = (float)_Component[0][0];
ret[0, 1] = (float)_Component[0][1];
ret[0, 2] = (float)_Component[0][2];
ret[1, 0] = (float)_Component[1][0];
ret[1, 1] = (float)_Component[1][1];
ret[1, 2] = (float)_Component[1][2];
ret[2, 0] = (float)_Component[2][0];
ret[2, 1] = (float)_Component[2][1];
ret[2, 2] = (float)_Component[2][2];
return(ret);
}
public RigidBody(Entity parent, string collision)
{
Parent = parent;
Collision = Model.LoadCollisionMesh(collision);
AABB = new BoundingBox(vec3.Zero, vec3.Zero);
//aabbMesh = Model.LoadCollisionMesh(collision);
UpdateAABB();
float tr = 1f / 6f * Parent.Transform.Scale.x;
float of = 0;
Inertia = new mat3(tr, of, of, of, tr, of, of, of, tr);
InverseInertia = Inertia.Inverse;
InverseInertiaWorldspace = InverseInertia;
}
public void ClipmapFragmentMain()
{
var light = Normalize(new vec3(0.0f, 1.0f, 0.6f));
var n = Normalize(Normal);
var n2 = Normalize(Cross(DeriveTowardsX(_finalPos.xyz), DeriveTowardsY(_finalPos.xyz)));
n2.xy = -n2.xy;
var light2 = new mat3(NormalMatrix) * (light);
var i = Max(Dot(light2, n2), 0.0f) * 0.8f + 0.2f; // Dot(light2, n2);
FragColor = Color * i;
}
/// <summary>
/// </summary>
/// <param name="uniformName"></param>
/// <param name="m"></param>
internal int glUniform(string uniformName, mat3 m)
{
int location = GetUniformLocation(uniformName);
if (location >= 0)
{
if (glUniformMatrix3fv == null)
{
glUniformMatrix3fv = GL.Instance.GetDelegateFor("glUniformMatrix3fv", GLDelegates.typeof_void_int_int_bool_floatN) as GLDelegates.void_int_int_bool_floatN;
}
float[] array = m.ToArray();
glUniformMatrix3fv(location, 1, false, array);
}
return(location);
}
private static void loadRoom(ref SceneManager sManager)
{
var triangleList = Parser.getTriangleListFromFile(Constants.Filepath_objectdata, "Room");
vec4 position = new vec4(0, 30, 0, 1);
vec3 scale = new vec3(3, 3, 3);
vec4 rotationAxis = new vec4(0, 1, 0, 1);
float angle = 0;
mat3 rotationMatrix = Calculation.calculateRotationMatrix(rotationAxis, angle);
var transformationMatrix = Calculation.calculateTransformationMatrix(position, rotationMatrix, scale);
TriangleObject room = new TriangleObject(objID, transformationMatrix, triangleList);
objID++;
sManager.addContent(room);
}
public void CanMultiplyByVector()
{
var m = new mat3(new[]
{
new vec3(1f, 2f, 3f),
new vec3(4f, 5f, 6f),
new vec3(7f, 8f, 9f),
});
var v = new vec3(10f, 11f, 12f);
// 1 4 7 10 10 + 44 + 84 138
// 2 5 8 * 11 = 20 + 55 + 96 = 171
// 3 6 9 12 30 + 66 + 108 204
Assert.AreEqual(new vec3(138f, 171f, 204f), m * v, "Rank 2 Matrix * Vector results are incorrect.");
}
public override void SetDeclarations(ref ShaderVariables shaderVars)
{
Matrix3 preRot = new Matrix3();
preRot.MakeFromRPY(_PreRotation.x, _PreRotation.y, _PreRotation.z);
mat3 glPreRot = preRot.GetGLMat3();
Matrix3 postRot = new Matrix3();
postRot.MakeFromRPY(_PostRotation.x, _PostRotation.y, _PostRotation.z);
mat3 glPostRot = postRot.GetGLMat3();
shaderVars.Add("fracScale" + _Iteration, (float)_Scale);
shaderVars.Add("fracOffset" + _Iteration, _Offset);
shaderVars.Add("fracPreRot" + _Iteration, glPreRot);
shaderVars.Add("fracPostRot" + _Iteration, glPostRot);
}
public bool GetUniformMat3ArrayValue(string varNameInShader, out mat3[] value)
{
value = null;
bool gotUniform = false;
foreach (var item in this.uniformVariables)
{
if (item.VarName == varNameInShader)
{
value = (item as UniformMat3Array).Value;
gotUniform = true;
break;
}
}
return gotUniform;
}
/// <summary>
/// Gets the inversed matrix.
/// <para>获取逆矩阵。</para>
/// </summary>
/// <param name="m"></param>
/// <returns></returns>
public static mat3 inverse(mat3 m)
{
float OneOverDeterminant = (1f) / (
+m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
- m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
+ m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]));
mat3 Inverse = new mat3(0);
Inverse[0, 0] = +(m[1][1] * m[2][2] - m[2][1] * m[1][2]) * OneOverDeterminant;
Inverse[1, 0] = -(m[1][0] * m[2][2] - m[2][0] * m[1][2]) * OneOverDeterminant;
Inverse[2, 0] = +(m[1][0] * m[2][1] - m[2][0] * m[1][1]) * OneOverDeterminant;
Inverse[0, 1] = -(m[0][1] * m[2][2] - m[2][1] * m[0][2]) * OneOverDeterminant;
Inverse[1, 1] = +(m[0][0] * m[2][2] - m[2][0] * m[0][2]) * OneOverDeterminant;
Inverse[2, 1] = -(m[0][0] * m[2][1] - m[2][0] * m[0][1]) * OneOverDeterminant;
Inverse[0, 2] = +(m[0][1] * m[1][2] - m[1][1] * m[0][2]) * OneOverDeterminant;
Inverse[1, 2] = -(m[0][0] * m[1][2] - m[1][0] * m[0][2]) * OneOverDeterminant;
Inverse[2, 2] = +(m[0][0] * m[1][1] - m[1][0] * m[0][1]) * OneOverDeterminant;
return Inverse;
}
/// <summary>
/// Build a look at view matrix.
/// transform object's coordinate from world's space to camera's space.
/// </summary>
/// <param name="eye">The eye.</param>
/// <param name="center">The center.</param>
/// <param name="up">Up.</param>
/// <returns></returns>
public static mat3 lookAt(vec2 eye, vec2 center, bool up)
{
// camera's back in world space coordinate system
vec2 back = (eye - center).normalize();
// camera's right in world space coordinate system
vec2 right = up.cross(back).normalize();
if (!up) { right = -right; }
mat3 viewMatrix = new mat3(1);
viewMatrix.col0.x = right.x;
viewMatrix.col1.x = right.y;
viewMatrix.col0.y = back.x;
viewMatrix.col1.y = back.y;
// Translation in world space coordinate system
viewMatrix.col3.x = -eye.dot(right);
viewMatrix.col3.y = -eye.dot(back);
return viewMatrix;
}
public static mat4 RotateMatrix(float angle, vec3 axis)
{
vec3 n = normalize(axis);
float theta = radians(angle);
float c = cos(theta);
float s = sin(theta);
mat3 R = new mat3();
R[0] = n * n.x * (1.0f - c) + new vec3(c, n.z * s, -n.y * s);
R[1] = n * n.y * (1.0f - c) + new vec3(-n.z * s, c, n.x * s);
R[2] = n * n.z * (1.0f - c) + new vec3(n.y * s, -n.x * s, c);
mat4 rValue = new mat4(
new vec4(R[0], 0.0f),
new vec4(R[1], 0.0f),
new vec4(R[2], 0.0f),
new vec4(0, 0, 0, 1));
return rValue;
}
public void MatrixIsColumnMajor()
{
// A pretty critical test as this is fundamental.
var m = new mat3(new [] {
new vec3(1f, 2f, 3f),
new vec3(4f, 5f, 6f),
new vec3(7f, 8f, 9f)
});
// 1 4 7
// 2 5 8
// 3 6 9
Assert.AreEqual(1f, m[0][0], "Matrix does not implement column major semantics");
Assert.AreEqual(2f, m[0][1], "Matrix does not implement column major semantics");
Assert.AreEqual(3f, m[0][2], "Matrix does not implement column major semantics");
Assert.AreEqual(4f, m[1][0], "Matrix does not implement column major semantics");
Assert.AreEqual(5f, m[1][1], "Matrix does not implement column major semantics");
Assert.AreEqual(6f, m[1][2], "Matrix does not implement column major semantics");
Assert.AreEqual(7f, m[2][0], "Matrix does not implement column major semantics");
Assert.AreEqual(8f, m[2][1], "Matrix does not implement column major semantics");
Assert.AreEqual(9f, m[2][2], "Matrix does not implement column major semantics");
Assert.AreEqual(1f, m[0, 0], "Matrix does not implement column major semantics");
Assert.AreEqual(2f, m[0, 1], "Matrix does not implement column major semantics");
Assert.AreEqual(3f, m[0, 2], "Matrix does not implement column major semantics");
Assert.AreEqual(4f, m[1, 0], "Matrix does not implement column major semantics");
Assert.AreEqual(5f, m[1, 1], "Matrix does not implement column major semantics");
Assert.AreEqual(6f, m[1, 2], "Matrix does not implement column major semantics");
Assert.AreEqual(7f, m[2, 0], "Matrix does not implement column major semantics");
Assert.AreEqual(8f, m[2, 1], "Matrix does not implement column major semantics");
Assert.AreEqual(9f, m[2, 2], "Matrix does not implement column major semantics");
Assert.AreEqual(new vec3(1f, 2f, 3f), m[0], "Matrix does not implement column major semantics");
Assert.AreEqual(new vec3(4f, 5f, 6f), m[1], "Matrix does not implement column major semantics");
Assert.AreEqual(new vec3(7f, 8f, 9f), m[2], "Matrix does not implement column major semantics");
}
/// <summary>
/// Multiply matrix x by matrix y component-wise, i.e., result[i][j] is the scalar product of x[i][j] and y[i][j].
/// Note: to get linear algebraic matrix multiplication, use the multiply operator (*).
/// </summary>
protected mat3 matrixCompMult(mat3 x, mat3 y)
{
throw _invalidAccess;
}
/// <summary>
/// Simplify the creation of the normal matrix by using a modelView.
/// </summary>
/// <param name="modelView"></param>
public void CreateFromModelView(ModelView modelView)
{
_normalMatrix = modelView.ModelviewMatrix.to_mat3();
}
/// <summary>
///
/// </summary>
/// <param name="varNameInShader"></param>
/// <param name="value"></param>
/// <returns></returns>
public bool GetUniformMat3ArrayValue(string varNameInShader, out mat3[] value)
{
//if ((!this.Initialized) && (!this.Initializing)) { this.Initialize(); }
value = null;
bool gotUniform = false;
foreach (UniformVariable item in this.uniformVariables)
{
if (item.VarName == varNameInShader)
{
value = (item as UniformMat3Array).Value.Array;
gotUniform = true;
break;
}
}
return gotUniform;
}
/// <summary>
/// </summary>
/// <param name="uniformName"></param>
/// <param name="m"></param>
public int SetUniformMatrix3(string uniformName, mat3[] m)
{
int location = GetUniformLocation(uniformName);
if (location >= 0)
{
if (glUniformMatrix3fv == null) { glUniformMatrix3fv = OpenGL.GetDelegateFor<OpenGL.glUniformMatrix3fv>(); }
var values = new float[m.Length * 9];
for (int index = 0, i = 0; i < m.Length; i++)
{
float[] array = m[i].ToArray();
for (int j = 0; j < 9; j++)
{
values[index++] = array[j];
}
}
glUniformMatrix3fv(location, m.Length / 9, false, values);
}
return location;
}
/// <summary>initialized the matrix with the upperleft part of m
/// sets the lower right diagonal component(s) to 1, everything else to 0</summary>
public mat3x4(mat3 m)
{
throw _invalidAccess;
}
/// <summary>
/// Gets the transposed matrix.
/// <para>获取转置矩阵。</para>
/// </summary>
/// <param name="m"></param>
/// <returns></returns>
public static mat3 transpose(mat3 m)
{
vec3 col0 = m.col0;
vec3 col1 = m.col1;
vec3 col2 = m.col2;
return new mat3(
new vec3(col0.x, col1.x, col2.x),
new vec3(col0.y, col1.y, col2.y),
new vec3(col0.z, col1.z, col2.z)
);
}
/// <summary>
/// Applies a translation transformation to matrix <paramref name="m"/> by vector <paramref name="v"/>.
/// </summary>
/// <param name="m">The matrix to transform.</param>
/// <param name="v">The vector to translate by.</param>
/// <returns><paramref name="m"/> translated by <paramref name="v"/>.</returns>
public static mat3 translate(mat3 m, vec2 v)
{
mat3 result = m;
result.col2 = m.col0 * v.x + m.col1 * v.y + m.col2;
return result;
}
/// <summary>
///
/// </summary>
/// <param name="varNameInShader"></param>
/// <param name="value"></param>
/// <returns></returns>
public bool SetUniform(string varNameInShader, mat3[] value)
{
//if ((!this.Initialized) && (!this.Initializing)) { this.Initialize(); }
bool gotUniform = false;
bool updated = false;
if (value.Length <= 0) { return updated; }
foreach (UniformVariable item in this.uniformVariables)
{
if (item.VarName == varNameInShader)
{
(item as UniformMat3Array).Value = new NoisyArray<mat3>(value);
updated = true;
gotUniform = true;
break;
}
}
if (!gotUniform)
{
//int location = Program.GetUniformLocation(varNameInShader);
//if (location < 0)
{
//throw new Exception(string.Format(
//"niform variable [{0}] not exists! Remember to invoke RendererBase.Initialize(); before this method.", varNameInShader));
}
var variable = GetVariableArray(value, varNameInShader) as UniformMat3Array;
variable.Value = new NoisyArray<mat3>(value);
this.uniformVariables.Add(variable);
updated = true;
}
return updated;
}
public bool SetUniform(string varNameInShader, mat3[] value)
{
bool gotUniform = false;
bool updated = false;
if (value.Length <= 0) { return updated; }
foreach (var item in this.uniformVariables)
{
if (item.VarName == varNameInShader)
{
(item as UniformMat3Array).Value = value;
updated = true;
gotUniform = true;
break;
}
}
if (!gotUniform)
{
int location = ShaderProgram.GetUniformLocation(varNameInShader);
if (location < 0)
{
throw new Exception(string.Format(
"uniform variable [{0}] not exists!", varNameInShader));
}
var variable = GetVariableArray(value, varNameInShader) as UniformMat3Array;
variable.Value = value;
this.uniformVariables.Add(variable);
updated = true;
}
return updated;
}
public void ClipmapFragmentMain()
{
var light = Normalize(new vec3(0.0f, 1.0f, 0.6f));
var n = Normalize(Normal);
var n2 = Normalize(Cross(DeriveTowardsX(_finalPos.xyz), DeriveTowardsY(_finalPos.xyz)));
n2.xy = -n2.xy;
var light2 = new mat3(NormalMatrix) * (light);
var i = Max(Dot(light2, n2), 0.0f) * 0.8f + 0.2f; // Dot(light2, n2);
FragColor = Color * i;
}
/// <summary>initialized the matrix with the upperleft part of m
/// sets the lower right diagonal component(s) to 1, everything else to 0</summary>
public mat4x3(mat3 m)
{
throw _invalidAccess;
}
/// <summary>
/// Returns a matrix that is the transpose of m.
/// The input matrix m is not modified.
/// </summary>
protected mat3 transpose(mat3 m)
{
throw _invalidAccess;
}
/// <summary>Returns the determinant of m. </summary>
protected float determinant(mat3 m)
{
throw _invalidAccess;
}