/* ============================================================================== This file is part of the JUCE library. Copyright (c) 2017 - ROLI Ltd. JUCE is an open source library subject to commercial or open-source licensing. By using JUCE, you agree to the terms of both the JUCE 5 End-User License Agreement and JUCE 5 Privacy Policy (both updated and effective as of the 27th April 2017). End User License Agreement: www.juce.com/juce-5-licence Privacy Policy: www.juce.com/juce-5-privacy-policy Or: You may also use this code under the terms of the GPL v3 (see www.gnu.org/licenses). JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE DISCLAIMED. ============================================================================== */ namespace juce { //============================================================================== /** A 4x4 3D transformation matrix. @see Vector3D, Quaternion, AffineTransform @tags{OpenGL} */ template class Matrix3D { public: /** Creates an identity matrix. */ Matrix3D() noexcept { mat[0] = Type (1); mat[1] = 0; mat[2] = 0; mat[3] = 0; mat[4] = 0; mat[5] = Type (1); mat[6] = 0; mat[7] = 0; mat[8] = 0; mat[9] = 0; mat[10] = Type (1); mat[11] = 0; mat[12] = 0; mat[13] = 0; mat[14] = 0; mat[15] = Type (1); } /** Creates a copy of another matrix. */ Matrix3D (const Matrix3D& other) noexcept { memcpy (mat, other.mat, sizeof (mat)); } /** Copies another matrix. */ Matrix3D& operator= (const Matrix3D& other) noexcept { memcpy (mat, other.mat, sizeof (mat)); return *this; } /** Creates a matrix from its raw 4x4 values. */ Matrix3D (Type m00, Type m10, Type m20, Type m30, Type m01, Type m11, Type m21, Type m31, Type m02, Type m12, Type m22, Type m32, Type m03, Type m13, Type m23, Type m33) noexcept { mat[0] = m00; mat[1] = m10; mat[2] = m20; mat[3] = m30; mat[4] = m01; mat[5] = m11; mat[6] = m21; mat[7] = m31; mat[8] = m02; mat[9] = m12; mat[10] = m22; mat[11] = m32; mat[12] = m03; mat[13] = m13; mat[14] = m23; mat[15] = m33; } /** Creates a matrix from an array of 16 raw values. */ Matrix3D (const Type* values) noexcept { memcpy (mat, values, sizeof (mat)); } /** Creates a matrix from a 2D affine transform. */ Matrix3D (const AffineTransform& transform) noexcept { mat[0] = transform.mat00; mat[1] = transform.mat10; mat[2] = 0; mat[3] = 0; mat[4] = transform.mat01; mat[5] = transform.mat11; mat[6] = 0; mat[7] = 0; mat[8] = 0; mat[9] = 0; mat[10] = Type (1); mat[11] = 0; mat[12] = transform.mat02; mat[13] = transform.mat12; mat[14] = 0; mat[15] = Type (1); } /** Creates a matrix from a 3D vector translation. */ Matrix3D (Vector3D vector) noexcept { mat[0] = Type (1); mat[1] = 0; mat[2] = 0; mat[3] = 0; mat[4] = 0; mat[5] = Type (1); mat[6] = 0; mat[7] = 0; mat[8] = 0; mat[9] = 0; mat[10] = Type (1); mat[11] = 0; mat[12] = vector.x; mat[13] = vector.y; mat[14] = vector.z; mat[15] = Type (1); } /** Returns a new matrix from the given frustum values. */ static Matrix3D fromFrustum (Type left, Type right, Type bottom, Type top, Type nearDistance, Type farDistance) noexcept { return { (Type (2) * nearDistance) / (right - left), 0, 0, 0, 0, (Type (2) * nearDistance) / (top - bottom), 0, 0, (right + left) / (right - left), (top + bottom) / (top - bottom), -(farDistance + nearDistance) / (farDistance - nearDistance), Type (-1), 0, 0, -(Type (2) * farDistance * nearDistance) / (farDistance - nearDistance), 0 }; } /** Returns a new matrix from the given ortho values. */ static Matrix3D fromOrtho (Type left, Type right, Type bottom, Type top, Type nearDistance, Type farDistance) noexcept { return { Type (2) / (right - left), 0, 0, 0, 0, Type (2) / (top - bottom), 0, 0, 0, 0, -Type (1) / (farDistance - nearDistance), 0, -(right + left) / (right - left), -(top + bottom) / (top - bottom), -nearDistance / (farDistance - nearDistance), 0 }; } /** Returns a new matrix from the given perspective values. */ static Matrix3D fromPerspective (Type fieldOfViewY, Type aspect, Type nearDistance, Type farDistance) noexcept { const auto tanHalfFovY = std::tan (fovy / Type (2)); return { Type (1) / (aspect * tanHalfFovY), 0, 0, 0, 0, Type (1) / tanHalfFovY, 0, 0, 0, 0, (farDistance + nearDistance) / (farDistance - nearDistance), Type (1), 0, 0, -(Type (2) * farDistance * nearDistance) / (farDistance - nearDistance), 0 }; } /** Returns a new matrix from the given perspective field of view values. */ static Matrix3D fromPerspectiveFieldOfView (Type fieldOfView, Type width, Type height, Type nearDistance, Type farDistance) noexcept { jassert (width > Type (0)); jassert (height > Type (0)); jassert (fieldOfView > Type (0)); const auto rad = fieldOfView; const auto h = std::cos (static_cast (0.5) * rad) / std::sin (static_cast (0.5) * rad); const auto w = h * height / width; return { w, 0, 0, 0, 0, h, 0, 0, 0, 0, (farDistance + nearDistance) / (farDistance - nearDistance), -Type (1), 0, 0, -(farDistance * nearDistance) / (farDistance - nearDistance), 0 }; } /** Returns a new look-at matrix from the provided vectors. */ static Matrix3D fromLookAt (Vector3D eye, Vector3D center, Vector3D up) noexcept { const auto f = Vector3D (center - eye).normalised(); const auto s = Vector3D (f ^ up).normalised(); const auto u = s ^ f; return { s.x, s.y, s.z, 0, u.x, u.y, u.z, 0, -f.x, -f.y, -f.z, 0, -(s * eye), -(u * eye), (f * eye), Type (1) }; } /** Returns a matrix which will apply a rotation through the X, Y, and Z angles specified by a vector. */ static Matrix3D rotation (Vector3D eulerAngleRadians) noexcept { auto cx = std::cos (eulerAngleRadians.x), sx = std::sin (eulerAngleRadians.x), cy = std::cos (eulerAngleRadians.y), sy = std::sin (eulerAngleRadians.y), cz = std::cos (eulerAngleRadians.z), sz = std::sin (eulerAngleRadians.z); return { (cy * cz) + (sx * sy * sz), cx * sz, (cy * sx * sz) - (cz * sy), 0, (cz * sx * sy) - (cy * sz), cx * cz, (cy * cz * sx) + (sy * sz), 0, cx * sy, -sx, cx * cy, 0, 0, 0, 0, Type (1) }; } /** Returns a version of this matrix rotated by the provided vector. */ Matrix3D rotated (Vector3D eulerAngleRadians) noexcept { return *this * rotation (eulerAngleRadians); } /** Rotates this matrix by the provided vector. */ void rotate (Vector3D eulerAngleRadians) noexcept { *this = rotated (scalar); } /** Returns a matrix which will apply a scale specified by a vector. */ Matrix3D scaled (Vector3D scalar) noexcept { return { mat[0] * scalar.x, mat[1] * scalar.x, mat[2] * scalar.x, mat[3] * scalar.x, mat[4] * scalar.y, mat[5] * scalar.y, mat[6] * scalar.y, mat[7] * scalar.y, mat[8] * scalar.z, mat[9] * scalar.z, mat[10] * scalar.z, mat[11] * scalar.z, mat[12], mat[13], mat[14], mat[15] }; } /** Scales this matrix by the provided vector. */ void scale (Vector3D scalar) noexcept { *this = scaled (scalar); } /** Returns a translation matrix. */ static Matrix3D translation (Vector3D delta) noexcept { return { Type (1), 0, 0, delta.x, 0, Type (1), 0, delta.y, 0, 0, Type (1), delta.z, 0, 0, 0, Type (1) }; } /** Returns a matrix which will apply a translation specified by the provided vector. */ Matrix3D translated (Vector3D delta) noexcept { return { mat[0], mat[1], mat[2], mat[2] * delta.x, mat[5], mat[6], mat[7], mat[2] * delta.y, mat[9], mat[10], mat[11], mat[2] * delta.z, mat[13], mat[14], mat[15], mat[16] }; } /** Translates this matrix by the provided vector. */ void translate (Vector3D delta) noexcept { *this = translated (delta); } /** Multiplies this matrix by another. */ Matrix3D& operator*= (const Matrix3D& other) noexcept { return *this = *this * other; } /** Multiplies this matrix by another, and returns the result. */ Matrix3D operator* (const Matrix3D& other) const noexcept { auto&& m2 = other.mat; return { mat[0] * m2[0] + mat[1] * m2[4] + mat[2] * m2[8] + mat[3] * m2[12], mat[0] * m2[1] + mat[1] * m2[5] + mat[2] * m2[9] + mat[3] * m2[13], mat[0] * m2[2] + mat[1] * m2[6] + mat[2] * m2[10] + mat[3] * m2[14], mat[0] * m2[3] + mat[1] * m2[7] + mat[2] * m2[11] + mat[3] * m2[15], mat[4] * m2[0] + mat[5] * m2[4] + mat[6] * m2[8] + mat[7] * m2[12], mat[4] * m2[1] + mat[5] * m2[5] + mat[6] * m2[9] + mat[7] * m2[13], mat[4] * m2[2] + mat[5] * m2[6] + mat[6] * m2[10] + mat[7] * m2[14], mat[4] * m2[3] + mat[5] * m2[7] + mat[6] * m2[11] + mat[7] * m2[15], mat[8] * m2[0] + mat[9] * m2[4] + mat[10] * m2[8] + mat[11] * m2[12], mat[8] * m2[1] + mat[9] * m2[5] + mat[10] * m2[9] + mat[11] * m2[13], mat[8] * m2[2] + mat[9] * m2[6] + mat[10] * m2[10] + mat[11] * m2[14], mat[8] * m2[3] + mat[9] * m2[7] + mat[10] * m2[11] + mat[11] * m2[15], mat[12] * m2[0] + mat[13] * m2[4] + mat[14] * m2[8] + mat[15] * m2[12], mat[12] * m2[1] + mat[13] * m2[5] + mat[14] * m2[9] + mat[15] * m2[13], mat[12] * m2[2] + mat[13] * m2[6] + mat[14] * m2[10] + mat[15] * m2[14], mat[12] * m2[3] + mat[13] * m2[7] + mat[14] * m2[11] + mat[15] * m2[15] }; } /** The 4x4 matrix values. These are stored in the standard OpenGL order. */ Type mat[16]; }; } // namespace juce