public static Matrix4f createViewMatrix(Vector3f AtVec, Vector3f EyeVec, Vector3f UpVec)
{
Matrix4f viewMatrix = Matrix4f.identity();
viewMatrix = lookAt(AtVec, EyeVec, UpVec);
return(viewMatrix);
}
public Matrix4f(Matrix4f matrix)
{
this._cols[0] = matrix._cols[0];
this._cols[1] = matrix._cols[1];
this._cols[2] = matrix._cols[2];
this._cols[3] = matrix._cols[3];
}
public static Matrix4f createProjectionMatrix(float FovY, float aspectRatio, float zNear, float zFar)
{
Matrix4f projectionMatrix = new Matrix4f(1);
projectionMatrix = perspective(Trigonometric.toRadians(FovY), aspectRatio, zNear, zFar);
return(projectionMatrix);
}
public static Matrix3f createNormalMatrix(Matrix4f viewMatrix, Matrix4f modelMatrix)
{
Matrix3f result;
result = MatrixTransforms.Transpose(MatrixTransforms.Inverse(viewMatrix * modelMatrix)).toMatrix3();
return(result);
}
/// <summary>
/// Builds a rotation 4 * 4 matrix created from an axis vector and an angle.
/// </summary>
/// <param name="m">The m.</param>
/// <param name="angle">The angle.</param>
/// <param name="v">The v.</param>
/// <returns></returns>
public static Matrix4f rotate(Matrix4f m, float angle, Vector3f v)
{
float c = Trigonometric.Cos(angle);
float s = Trigonometric.Sin(angle);
Vector3f axis = Geometric.Normalize(v);
Vector3f temp = (1.0f - c) * axis;
Matrix4f rotate = Matrix4f.identity();
rotate[0, 0] = c + temp[0] * axis[0];
rotate[0, 1] = 0 + temp[0] * axis[1] + s * axis[2];
rotate[0, 2] = 0 + temp[0] * axis[2] - s * axis[1];
rotate[1, 0] = 0 + temp[1] * axis[0] - s * axis[2];
rotate[1, 1] = c + temp[1] * axis[1];
rotate[1, 2] = 0 + temp[1] * axis[2] + s * axis[0];
rotate[2, 0] = 0 + temp[2] * axis[0] + s * axis[1];
rotate[2, 1] = 0 + temp[2] * axis[1] - s * axis[0];
rotate[2, 2] = c + temp[2] * axis[2];
Matrix4f result = Matrix4f.identity();
result[0] = m[0] * rotate[0][0] + m[1] * rotate[0][1] + m[2] * rotate[0][2];
result[1] = m[0] * rotate[1][0] + m[1] * rotate[1][1] + m[2] * rotate[1][2];
result[2] = m[0] * rotate[2][0] + m[1] * rotate[2][1] + m[2] * rotate[2][2];
result[3] = m[3];
return(result);
}
/// <summary>
/// Multiplies the <paramref name="lhs"/> matrix by the <paramref name="rhs"/> matrix.
/// </summary>
/// <param name="lhs">The LHS matrix.</param>
/// <param name="rhs">The RHS matrix.</param>
/// <returns>The product of <paramref name="lhs"/> and <paramref name="rhs"/>.</returns>
public static Matrix4f operator *(Matrix4f lhs, Matrix4f rhs)
{
Matrix4f tempM = new Matrix4f(0);
tempM[0][0] = (lhs[0][0] * rhs[0][0]) + (lhs[0][1] * rhs[1][0]) + (lhs[0][2] * rhs[2][0]) + (lhs[0][3] * rhs[3][0]);
tempM[1][0] = (lhs[1][0] * rhs[0][0]) + (lhs[1][1] * rhs[1][0]) + (lhs[1][2] * rhs[2][0]) + (lhs[1][3] * rhs[3][0]);
tempM[2][0] = (lhs[2][0] * rhs[0][0]) + (lhs[2][1] * rhs[1][0]) + (lhs[2][2] * rhs[2][0]) + (lhs[2][3] * rhs[3][0]);
tempM[3][0] = (lhs[3][0] * rhs[0][0]) + (lhs[3][1] * rhs[1][0]) + (lhs[3][2] * rhs[2][0]) + (lhs[3][3] * rhs[3][0]);
tempM[0][1] = (lhs[0][0] * rhs[0][1]) + (lhs[0][1] * rhs[1][1]) + (lhs[0][2] * rhs[2][1]) + (lhs[0][3] * rhs[3][1]);
tempM[1][1] = (lhs[1][0] * rhs[0][1]) + (lhs[1][1] * rhs[1][1]) + (lhs[1][2] * rhs[2][1]) + (lhs[1][3] * rhs[3][1]);
tempM[2][1] = (lhs[2][0] * rhs[0][1]) + (lhs[2][1] * rhs[1][1]) + (lhs[2][2] * rhs[2][1]) + (lhs[2][3] * rhs[3][1]);
tempM[3][1] = (lhs[3][0] * rhs[0][1]) + (lhs[3][1] * rhs[1][1]) + (lhs[3][2] * rhs[2][1]) + (lhs[3][3] * rhs[3][1]);
tempM[0][2] = (lhs[0][0] * rhs[0][2]) + (lhs[0][1] * rhs[1][2]) + (lhs[0][2] * rhs[2][2]) + (lhs[0][3] * rhs[3][2]);
tempM[1][2] = (lhs[1][0] * rhs[0][2]) + (lhs[1][1] * rhs[1][2]) + (lhs[1][2] * rhs[2][2]) + (lhs[1][3] * rhs[3][2]);
tempM[2][2] = (lhs[2][0] * rhs[0][2]) + (lhs[2][1] * rhs[1][2]) + (lhs[2][2] * rhs[2][2]) + (lhs[2][3] * rhs[3][2]);
tempM[3][2] = (lhs[3][0] * rhs[0][2]) + (lhs[3][1] * rhs[1][2]) + (lhs[3][2] * rhs[2][2]) + (lhs[3][3] * rhs[3][2]);
tempM[0][3] = (lhs[0][0] * rhs[0][3]) + (lhs[0][1] * rhs[1][3]) + (lhs[0][2] * rhs[2][3]) + (lhs[0][3] * rhs[3][3]);
tempM[1][3] = (lhs[1][0] * rhs[0][3]) + (lhs[1][1] * rhs[1][3]) + (lhs[1][2] * rhs[2][3]) + (lhs[1][3] * rhs[3][3]);
tempM[2][3] = (lhs[2][0] * rhs[0][3]) + (lhs[2][1] * rhs[1][3]) + (lhs[2][2] * rhs[2][3]) + (lhs[2][3] * rhs[3][3]);
tempM[3][3] = (lhs[3][0] * rhs[0][3]) + (lhs[3][1] * rhs[1][3]) + (lhs[3][2] * rhs[2][3]) + (lhs[3][3] * rhs[3][3]);
return(tempM);
}
/// <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 Matrix4f translate(Matrix4f m, Vector3f v)
{
Matrix4f result = m;
result[3] = (m[0] * v[0]) + (m[1] * v[1]) + (m[2] * v[2]) + m[3];
result[3][3] = 1.0f;
return(result);
}
public static Matrix4f Inverse(Matrix4f m)
{
float Coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
float Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
float Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
float Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
float Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
float Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
float Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
float Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
float Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
float Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
float Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
float Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
float Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
float Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
float Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
float Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
float Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
float Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
Vector4f Fac0 = new Vector4f(Coef00, Coef00, Coef02, Coef03);
Vector4f Fac1 = new Vector4f(Coef04, Coef04, Coef06, Coef07);
Vector4f Fac2 = new Vector4f(Coef08, Coef08, Coef10, Coef11);
Vector4f Fac3 = new Vector4f(Coef12, Coef12, Coef14, Coef15);
Vector4f Fac4 = new Vector4f(Coef16, Coef16, Coef18, Coef19);
Vector4f Fac5 = new Vector4f(Coef20, Coef20, Coef22, Coef23);
Vector4f Vec0 = new Vector4f(m[1][0], m[0][0], m[0][0], m[0][0]);
Vector4f Vec1 = new Vector4f(m[1][1], m[0][1], m[0][1], m[0][1]);
Vector4f Vec2 = new Vector4f(m[1][2], m[0][2], m[0][2], m[0][2]);
Vector4f Vec3 = new Vector4f(m[1][3], m[0][3], m[0][3], m[0][3]);
Vector4f Inv0 = new Vector4f(Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
Vector4f Inv1 = new Vector4f(Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
Vector4f Inv2 = new Vector4f(Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
Vector4f Inv3 = new Vector4f(Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);
Vector4f SignA = new Vector4f(+1, -1, +1, -1);
Vector4f SignB = new Vector4f(-1, +1, -1, +1);
Matrix4f inverse = new Matrix4f(Inv0 * SignA, Inv1 * SignB, Inv2 * SignA, Inv3 * SignB);
Vector4f Row0 = new Vector4f(inverse[0][0], inverse[1][0], inverse[2][0], inverse[3][0]);
Vector4f Dot0 = new Vector4f(m[0] * Row0);
float Dot1 = (Dot0.x + Dot0.y) + (Dot0.z + Dot0.w);
float OneOverDeterminant = (1f) / Dot1;
return(inverse * OneOverDeterminant);
}
/// <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 Matrix4f scale(Matrix4f m, Vector3f v)
{
Matrix4f result = m;
result[0] = m[0] * v[0];
result[1] = m[1] * v[1];
result[2] = m[2] * v[2];
result[3] = m[3];
return(result);
}
public static Matrix4f createModelMatrix(Vector3f translation, Vector3f rotate, Vector3f scale)
{
Matrix4f modelMatrix = Matrix4f.identity();
modelMatrix = translate(modelMatrix, translation);
modelMatrix = MatrixMath.rotate(modelMatrix, Trigonometric.toRadians(rotate.x), new Vector3f(1, 0, 0));
modelMatrix = MatrixMath.rotate(modelMatrix, Trigonometric.toRadians(rotate.y), new Vector3f(0, 1, 0));
modelMatrix = MatrixMath.rotate(modelMatrix, Trigonometric.toRadians(rotate.z), new Vector3f(0, 0, 1));
modelMatrix = MatrixMath.scale(modelMatrix, scale);
return(modelMatrix);
}
/// <summary>
/// Creates a matrix for projecting two-dimensional coordinates onto the screen.
/// </summary>
/// <param name="left">The left.</param>
/// <param name="right">The right.</param>
/// <param name="bottom">The bottom.</param>
/// <param name="top">The top.</param>
/// <returns></returns>
public static Matrix4f ortho(float left, float right, float bottom, float top)
{
var result = new Matrix4f(1);
result[0, 0] = (2f) / (right - left);
result[1, 1] = (2f) / (top - bottom);
result[2, 2] = -(1f);
result[3, 0] = -(right + left) / (right - left);
result[3, 1] = -(top + bottom) / (top - bottom);
return(result);
}
/// <summary>
/// Creates a frustrum projection matrix.
/// </summary>
/// <param name="left">The left.</param>
/// <param name="right">The right.</param>
/// <param name="bottom">The bottom.</param>
/// <param name="top">The top.</param>
/// <param name="nearVal">The near val.</param>
/// <param name="farVal">The far val.</param>
/// <returns></returns>
public static Matrix4f frustum(float left, float right, float bottom, float top, float nearVal, float farVal)
{
var result = new Matrix4f(1);
result[0, 0] = (2.0f * nearVal) / (right - left);
result[1, 1] = (2.0f * nearVal) / (top - bottom);
result[2, 0] = (right + left) / (right - left);
result[2, 1] = (top + bottom) / (top - bottom);
result[2, 2] = -(farVal + nearVal) / (farVal - nearVal);
result[2, 3] = -1.0f;
result[3, 2] = -(2.0f * farVal * nearVal) / (farVal - nearVal);
return(result);
}
/// <summary>
/// Creates a perspective transformation matrix.
/// </summary>
/// <param name="fovy">The field of view angle, in radians.</param>
/// <param name="aspect">The aspect ratio.</param>
/// <param name="zNear">The near depth clipping plane.</param>
/// <param name="zFar">The far depth clipping plane.</param>
/// <returns>A <see cref="mat4"/> that contains the projection matrix for the perspective transformation.</returns>
public static Matrix4f perspective(float fovy, float aspect, float zNear, float zFar)
{
var tanHalfFovy = (float)Math.Tan(fovy / 2.0f);
Matrix4f result = new Matrix4f(1.0f);
result[0, 0] = 1.0f / (aspect * tanHalfFovy);
result[1, 1] = 1.0f / (tanHalfFovy);
result[2, 2] = -(zFar + zNear) / (zFar - zNear);
result[2, 3] = -1.0f;
result[3, 2] = -(2.0f * zFar * zNear) / (zFar - zNear);
return(result);
}
/// <summary>
/// Map the specified object coordinates (obj.x, obj.y, obj.z) into window coordinates.
/// </summary>
/// <param name="obj">The object.</param>
/// <param name="model">The model.</param>
/// <param name="proj">The proj.</param>
/// <param name="viewport">The viewport.</param>
/// <returns></returns>
public static Vector3f project(Vector3f obj, Matrix4f model, Matrix4f proj, Vector4f viewport)
{
Vector4f tmp = new Vector4f(obj, (1f));
tmp = model * tmp;
tmp = proj * tmp;
tmp /= tmp.w;
tmp = tmp * 0.5f + 0.5f;
tmp[0] = tmp[0] * viewport[2] + viewport[0];
tmp[1] = tmp[1] * viewport[3] + viewport[1];
return(new Vector3f(tmp.x, tmp.y, tmp.z));
}
public static Matrix4f Transpose(Matrix4f m)
{
Vector4f[] vec = new Vector4f[4];
vec[0] = new Vector4f(m[0]);
vec[1] = new Vector4f(m[1]);
vec[2] = new Vector4f(m[2]);
vec[3] = new Vector4f(m[3]);
for (int i = 0; i < vec.Length; i++)
{
for (int j = 0; j < vec.Length; j++)
{
m[i][j] = vec[j][i];
}
}
return(m);
}
/// <summary>
/// Map the specified window coordinates (win.x, win.y, win.z) into object coordinates.
/// </summary>
/// <param name="win">The win.</param>
/// <param name="model">The model.</param>
/// <param name="proj">The proj.</param>
/// <param name="viewport">The viewport.</param>
/// <returns></returns>
public static Vector3f unProject(Vector3f win, Matrix4f model, Matrix4f proj, Vector4f viewport)
{
Matrix4f Inverse = MatrixTransforms.Inverse(proj * model);
Vector4f tmp = new Vector4f(win, (1f));
tmp.x = (tmp.x - (viewport[0])) / (viewport[2]);
tmp.y = (tmp.y - (viewport[1])) / (viewport[3]);
tmp = tmp * (2f) - (1f);
Vector4f obj = Inverse * tmp;
obj /= obj.w;
return(new Vector3f(obj));
}
/// <summary>
/// Creates a matrix for a symmetric perspective-view frustum with far plane
/// at infinite for graphics hardware that doesn't support depth clamping.
/// </summary>
/// <param name="fovy">The fovy.</param>
/// <param name="aspect">The aspect.</param>
/// <param name="zNear">The z near.</param>
/// <returns></returns>
public static Matrix4f tweakedInfinitePerspective(float fovy, float aspect, float zNear)
{
float range = Trigonometric.Tan(fovy / (2)) * zNear;
float left = -range * aspect;
float right = range * aspect;
float bottom = -range;
float top = range;
Matrix4f Result = new Matrix4f((0f));
Result[0, 0] = ((2) * zNear) / (right - left);
Result[1, 1] = ((2) * zNear) / (top - bottom);
Result[2, 2] = (0.0001f) - (1f);
Result[2, 3] = (-1);
Result[3, 2] = -((0.0001f) - (2)) * zNear;
return(Result);
}
/// <summary>
/// Creates a matrix for a symmetric perspective-view frustum with far plane at infinite.
/// </summary>
/// <param name="fovy">The fovy.</param>
/// <param name="aspect">The aspect.</param>
/// <param name="zNear">The z near.</param>
/// <returns></returns>
public static Matrix4f infinitePerspective(float fovy, float aspect, float zNear)
{
float range = Trigonometric.Tan(fovy / (2f)) * zNear;
float left = -range * aspect;
float right = range * aspect;
float bottom = -range;
float top = range;
var result = new Matrix4f(0);
result[0, 0] = ((2f) * zNear) / (right - left);
result[1, 1] = ((2f) * zNear) / (top - bottom);
result[2, 2] = -(1f);
result[2, 3] = -(1f);
result[3, 2] = -(2f) * zNear;
return(result);
}
/// <summary>
/// Builds a perspective projection matrix based on a field of view.
/// </summary>
/// <param name="fov">The fov (in radians).</param>
/// <param name="width">The width.</param>
/// <param name="height">The height.</param>
/// <param name="zNear">The z near.</param>
/// <param name="zFar">The z far.</param>
/// <returns></returns>
/// <exception cref="System.ArgumentOutOfRangeException"></exception>
public static Matrix4f perspectiveFov(float fov, float width, float height, float zNear, float zFar)
{
if (width <= 0 || height <= 0 || fov <= 0)
{
throw new ArgumentOutOfRangeException();
}
var rad = fov;
var h = Trigonometric.Cos((0.5f) * rad) / Trigonometric.Sin((0.5f) * rad);
var w = h * height / width;
var result = new Matrix4f(0);
result[0, 0] = w;
result[1, 1] = h;
result[2, 2] = -(zFar + zNear) / (zFar - zNear);
result[2, 3] = -(1f);
result[3, 2] = -((2f) * zFar * zNear) / (zFar - zNear);
return(result);
}
/// <summary>
/// Define a picking region.
/// </summary>
/// <param name="center">The center.</param>
/// <param name="delta">The delta.</param>
/// <param name="viewport">The viewport.</param>
/// <returns></returns>
/// <exception cref="System.ArgumentOutOfRangeException"></exception>
public static Matrix4f pickMatrix(Vector2f center, Vector2f delta, Vector4f viewport)
{
if (delta.x <= 0 || delta.y <= 0)
{
throw new ArgumentOutOfRangeException();
}
var Result = new Matrix4f(1.0f);
if (!(delta.x > (0f) && delta.y > (0f)))
{
return(Result); // Error
}
Vector3f Temp = new Vector3f(
((viewport[2]) - (2f) * (center.x - (viewport[0]))) / delta.x,
((viewport[3]) - (2f) * (center.y - (viewport[1]))) / delta.y,
(0f));
// Translate and scale the picked region to the entire window
Result = translate(Result, Temp);
return(scale(Result, new Vector3f((viewport[2]) / delta.x, (viewport[3]) / delta.y, (1))));
}
/// <summary>
/// Build a look at view matrix.
/// </summary>
/// <param name="eye">The eye.</param>
/// <param name="center">The center.</param>
/// <param name="up">Up.</param>
/// <returns></returns>
public static Matrix4f lookAt(Vector3f eye, Vector3f center, Vector3f up)
{
Vector3f f = new Vector3f(Geometric.Normalize(center - eye));
Vector3f s = new Vector3f(Geometric.Normalize(Geometric.cross(f, up)));
Vector3f u = new Vector3f(Geometric.cross(s, f));
Matrix4f Result = new Matrix4f(1);
Result[0, 0] = s.x;
Result[1, 0] = s.y;
Result[2, 0] = s.z;
Result[0, 1] = u.x;
Result[1, 1] = u.y;
Result[2, 1] = u.z;
Result[0, 2] = -f.x;
Result[1, 2] = -f.y;
Result[2, 2] = -f.z;
Result[3, 0] = -Geometric.Dot(s, eye);
Result[3, 1] = -Geometric.Dot(u, eye);
Result[3, 2] = Geometric.Dot(f, eye);
return(Result);
}
public static Matrix4f rotate(float angle, Vector3f v)
{
return(rotate(Matrix4f.identity(), angle, v));
}