Merge pull request #66388 from aaronfranke/3.x-cs-basis-euler
[3.x] C#: Add Basis Euler angle code to match 4.x core
This commit is contained in:
Rémi Verschelde
commit
abefe178c6
1 changed files with 352 additions and 23 deletions
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@ -8,6 +8,21 @@ using System.Runtime.InteropServices;
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namespace Godot
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{
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/// <summary>
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/// Specifies which order Euler angle rotations should be in.
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/// When composing, the order is the same as the letters. When decomposing,
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/// the order is reversed (ex: YXZ decomposes Z first, then X, and Y last).
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/// </summary>
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public enum EulerOrder
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{
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XYZ,
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XZY,
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YXZ,
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YZX,
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ZXY,
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ZYX
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};
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/// <summary>
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/// 3×3 matrix used for 3D rotation and scale.
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/// Almost always used as an orthogonal basis for a Transform.
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@ -272,41 +287,264 @@ namespace Godot
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/// The returned vector contains the rotation angles in
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/// the format (X angle, Y angle, Z angle).
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///
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/// Consider using the <see cref="Quat()"/> method instead, which
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/// Consider using the <see cref="RotationQuat"/> method instead, which
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/// returns a <see cref="Godot.Quat"/> quaternion instead of Euler angles.
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/// </summary>
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/// <returns>A <see cref="Vector3"/> representing the basis rotation in Euler angles.</returns>
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public Vector3 GetEuler()
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{
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Basis m = Orthonormalized();
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return GetEuler(EulerOrder.YXZ);
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}
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/// <summary>
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/// Returns the basis's rotation in the form of Euler angles.
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/// The Euler order depends on the [param order] parameter,
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/// for example using the YXZ convention: when decomposing,
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/// first Z, then X, and Y last. The returned vector contains
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/// the rotation angles in the format (X angle, Y angle, Z angle).
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///
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/// Consider using the <see cref="RotationQuat"/> method instead, which
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/// returns a <see cref="Godot.Quat"/> quaternion instead of Euler angles.
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/// </summary>
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/// <param name="order">The Euler order to use.</param>
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/// <returns>A <see cref="Vector3"/> representing the basis rotation in Euler angles.</returns>
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public Vector3 GetEuler(EulerOrder order)
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{
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switch (order)
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{
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case EulerOrder.XYZ:
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{
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// Euler angles in XYZ convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cy*cz -cy*sz sy
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// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
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// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
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Vector3 euler;
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real_t sy = Row0[2];
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if (sy < (1.0f - Mathf.Epsilon))
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{
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if (sy > -(1.0f - Mathf.Epsilon))
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{
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// is this a pure Y rotation?
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if (Row1[0] == 0 && Row0[1] == 0 && Row1[2] == 0 && Row2[1] == 0 && Row1[1] == 1)
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{
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// return the simplest form (human friendlier in editor and scripts)
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euler.x = 0;
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euler.y = Mathf.Atan2(Row0[2], Row0[0]);
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euler.z = 0;
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}
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else
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{
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euler.x = Mathf.Atan2(-Row1[2], Row2[2]);
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euler.y = Mathf.Asin(sy);
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euler.z = Mathf.Atan2(-Row0[1], Row0[0]);
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}
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}
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else
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{
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euler.x = Mathf.Atan2(Row2[1], Row1[1]);
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euler.y = -Mathf.Tau / 4.0f;
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euler.z = 0.0f;
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real_t mzy = m.Row1[2];
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if (mzy < 1.0f)
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{
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if (mzy > -1.0f)
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{
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euler.x = Mathf.Asin(-mzy);
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euler.y = Mathf.Atan2(m.Row0[2], m.Row2[2]);
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euler.z = Mathf.Atan2(m.Row1[0], m.Row1[1]);
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}
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else
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{
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euler.x = Mathf.Pi * 0.5f;
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euler.y = -Mathf.Atan2(-m.Row0[1], m.Row0[0]);
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}
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}
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else
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{
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euler.x = -Mathf.Pi * 0.5f;
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euler.y = -Mathf.Atan2(-m.Row0[1], m.Row0[0]);
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euler.x = Mathf.Atan2(Row2[1], Row1[1]);
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euler.y = Mathf.Tau / 4.0f;
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euler.z = 0.0f;
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}
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return euler;
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}
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case EulerOrder.XZY:
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{
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// Euler angles in XZY convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cz*cy -sz cz*sy
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// sx*sy+cx*cy*sz cx*cz cx*sz*sy-cy*sx
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// cy*sx*sz cz*sx cx*cy+sx*sz*sy
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Vector3 euler;
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real_t sz = Row0[1];
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if (sz < (1.0f - Mathf.Epsilon))
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{
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if (sz > -(1.0f - Mathf.Epsilon))
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{
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euler.x = Mathf.Atan2(Row2[1], Row1[1]);
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euler.y = Mathf.Atan2(Row0[2], Row0[0]);
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euler.z = Mathf.Asin(-sz);
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}
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else
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{
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// It's -1
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euler.x = -Mathf.Atan2(Row1[2], Row2[2]);
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euler.y = 0.0f;
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euler.z = Mathf.Tau / 4.0f;
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}
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}
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else
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{
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// It's 1
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euler.x = -Mathf.Atan2(Row1[2], Row2[2]);
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euler.y = 0.0f;
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euler.z = -Mathf.Tau / 4.0f;
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}
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return euler;
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}
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case EulerOrder.YXZ:
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{
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// Euler angles in YXZ convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cy*cz+sy*sx*sz cz*sy*sx-cy*sz cx*sy
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// cx*sz cx*cz -sx
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// cy*sx*sz-cz*sy cy*cz*sx+sy*sz cy*cx
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Vector3 euler;
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real_t m12 = Row1[2];
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if (m12 < (1 - Mathf.Epsilon))
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{
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if (m12 > -(1 - Mathf.Epsilon))
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{
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// is this a pure X rotation?
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if (Row1[0] == 0 && Row0[1] == 0 && Row0[2] == 0 && Row2[0] == 0 && Row0[0] == 1)
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{
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// return the simplest form (human friendlier in editor and scripts)
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euler.x = Mathf.Atan2(-m12, Row1[1]);
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euler.y = 0;
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euler.z = 0;
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}
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else
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{
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euler.x = Mathf.Asin(-m12);
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euler.y = Mathf.Atan2(Row0[2], Row2[2]);
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euler.z = Mathf.Atan2(Row1[0], Row1[1]);
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}
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}
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else
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{ // m12 == -1
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euler.x = Mathf.Tau / 4.0f;
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euler.y = Mathf.Atan2(Row0[1], Row0[0]);
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euler.z = 0;
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}
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}
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else
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{ // m12 == 1
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euler.x = -Mathf.Tau / 4.0f;
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euler.y = -Mathf.Atan2(Row0[1], Row0[0]);
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euler.z = 0;
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}
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return euler;
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}
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case EulerOrder.YZX:
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{
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// Euler angles in YZX convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cy*cz sy*sx-cy*cx*sz cx*sy+cy*sz*sx
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// sz cz*cx -cz*sx
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// -cz*sy cy*sx+cx*sy*sz cy*cx-sy*sz*sx
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Vector3 euler;
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real_t sz = Row1[0];
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if (sz < (1.0f - Mathf.Epsilon))
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{
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if (sz > -(1.0f - Mathf.Epsilon))
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{
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euler.x = Mathf.Atan2(-Row1[2], Row1[1]);
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euler.y = Mathf.Atan2(-Row2[0], Row0[0]);
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euler.z = Mathf.Asin(sz);
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}
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else
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{
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// It's -1
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euler.x = Mathf.Atan2(Row2[1], Row2[2]);
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euler.y = 0.0f;
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euler.z = -Mathf.Tau / 4.0f;
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}
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}
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else
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{
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// It's 1
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euler.x = Mathf.Atan2(Row2[1], Row2[2]);
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euler.y = 0.0f;
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euler.z = Mathf.Tau / 4.0f;
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}
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return euler;
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}
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case EulerOrder.ZXY:
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{
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// Euler angles in ZXY convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cz*cy-sz*sx*sy -cx*sz cz*sy+cy*sz*sx
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// cy*sz+cz*sx*sy cz*cx sz*sy-cz*cy*sx
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// -cx*sy sx cx*cy
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Vector3 euler;
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real_t sx = Row2[1];
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if (sx < (1.0f - Mathf.Epsilon))
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{
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if (sx > -(1.0f - Mathf.Epsilon))
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{
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euler.x = Mathf.Asin(sx);
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euler.y = Mathf.Atan2(-Row2[0], Row2[2]);
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euler.z = Mathf.Atan2(-Row0[1], Row1[1]);
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}
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else
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{
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// It's -1
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euler.x = -Mathf.Tau / 4.0f;
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euler.y = Mathf.Atan2(Row0[2], Row0[0]);
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euler.z = 0;
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}
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}
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else
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{
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// It's 1
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euler.x = Mathf.Tau / 4.0f;
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euler.y = Mathf.Atan2(Row0[2], Row0[0]);
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euler.z = 0;
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}
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return euler;
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}
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case EulerOrder.ZYX:
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{
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// Euler angles in ZYX convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cz*cy cz*sy*sx-cx*sz sz*sx+cz*cx*cy
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// cy*sz cz*cx+sz*sy*sx cx*sz*sy-cz*sx
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// -sy cy*sx cy*cx
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Vector3 euler;
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real_t sy = Row2[0];
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if (sy < (1.0f - Mathf.Epsilon))
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{
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if (sy > -(1.0f - Mathf.Epsilon))
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{
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euler.x = Mathf.Atan2(Row2[1], Row2[2]);
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euler.y = Mathf.Asin(-sy);
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euler.z = Mathf.Atan2(Row1[0], Row0[0]);
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}
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else
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{
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// It's -1
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euler.x = 0;
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euler.y = Mathf.Tau / 4.0f;
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euler.z = -Mathf.Atan2(Row0[1], Row1[1]);
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}
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}
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else
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{
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// It's 1
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euler.x = 0;
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euler.y = -Mathf.Tau / 4.0f;
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euler.z = -Mathf.Atan2(Row0[1], Row1[1]);
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}
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return euler;
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}
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default:
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throw new ArgumentOutOfRangeException(nameof(order));
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}
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}
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/// <summary>
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/// Get rows by index. Rows are not very useful for user code,
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@ -635,7 +873,7 @@ namespace Godot
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/// <summary>
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/// Returns the basis's rotation in the form of a quaternion.
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/// See <see cref="GetEuler()"/> if you need Euler angles, but keep in
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/// See <see cref="GetEuler"/> if you need Euler angles, but keep in
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/// mind that quaternions should generally be preferred to Euler angles.
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/// </summary>
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/// <returns>A <see cref="Godot.Quat"/> representing the basis's rotation.</returns>
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@ -860,6 +1098,62 @@ namespace Godot
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Row2 = new Vector3(xz, yz, zz);
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}
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/// <summary>
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/// Constructs a Basis matrix from Euler angles in the specified rotation order. By default, use YXZ order (most common).
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/// </summary>
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/// <param name="euler">The Euler angles to use.</param>
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/// <param name="order">The order to compose the Euler angles.</param>
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public static Basis FromEuler(Vector3 euler, EulerOrder order = EulerOrder.YXZ)
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{
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real_t c, s;
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c = Mathf.Cos(euler.x);
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s = Mathf.Sin(euler.x);
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Basis xmat = new Basis(new Vector3(1, 0, 0), new Vector3(0, c, s), new Vector3(0, -s, c));
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c = Mathf.Cos(euler.y);
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s = Mathf.Sin(euler.y);
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Basis ymat = new Basis(new Vector3(c, 0, -s), new Vector3(0, 1, 0), new Vector3(s, 0, c));
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c = Mathf.Cos(euler.z);
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s = Mathf.Sin(euler.z);
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Basis zmat = new Basis(new Vector3(c, s, 0), new Vector3(-s, c, 0), new Vector3(0, 0, 1));
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switch (order)
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{
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case EulerOrder.XYZ:
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return xmat * ymat * zmat;
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case EulerOrder.XZY:
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return xmat * zmat * ymat;
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case EulerOrder.YXZ:
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return ymat * xmat * zmat;
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case EulerOrder.YZX:
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return ymat * zmat * xmat;
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case EulerOrder.ZXY:
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return zmat * xmat * ymat;
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case EulerOrder.ZYX:
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return zmat * ymat * xmat;
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default:
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throw new ArgumentOutOfRangeException(nameof(order));
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}
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}
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/// <summary>
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/// Constructs a pure scale basis matrix with no rotation or shearing.
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/// The scale values are set as the main diagonal of the matrix,
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/// and all of the other parts of the matrix are zero.
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/// </summary>
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/// <param name="scale">The scale Vector3.</param>
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/// <returns>A pure scale Basis matrix.</returns>
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public static Basis FromScale(Vector3 scale)
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{
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return new Basis(
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scale.x, 0, 0,
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0, scale.y, 0,
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0, 0, scale.z
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);
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}
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/// <summary>
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/// Composes these two basis matrices by multiplying them
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/// together. This has the effect of transforming the second basis
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@ -878,6 +1172,41 @@ namespace Godot
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);
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}
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/// <summary>
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/// Returns a Vector3 transformed (multiplied) by the basis matrix.
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/// </summary>
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/// <param name="basis">The basis matrix transformation to apply.</param>
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/// <param name="vector">A Vector3 to transform.</param>
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/// <returns>The transformed Vector3.</returns>
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public static Vector3 operator *(Basis basis, Vector3 vector)
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{
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return new Vector3
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(
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basis.Row0.Dot(vector),
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basis.Row1.Dot(vector),
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basis.Row2.Dot(vector)
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);
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}
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/// <summary>
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/// Returns a Vector3 transformed (multiplied) by the transposed basis matrix.
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///
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/// Note: This results in a multiplication by the inverse of the
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/// basis matrix only if it represents a rotation-reflection.
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/// </summary>
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/// <param name="vector">A Vector3 to inversely transform.</param>
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/// <param name="basis">The basis matrix transformation to apply.</param>
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/// <returns>The inversely transformed vector.</returns>
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public static Vector3 operator *(Vector3 vector, Basis basis)
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{
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return new Vector3
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(
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basis.Row0[0] * vector.x + basis.Row1[0] * vector.y + basis.Row2[0] * vector.z,
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basis.Row0[1] * vector.x + basis.Row1[1] * vector.y + basis.Row2[1] * vector.z,
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basis.Row0[2] * vector.x + basis.Row1[2] * vector.y + basis.Row2[2] * vector.z
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);
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}
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/// <summary>
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/// Returns <see langword="true"/> if the basis matrices are exactly
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/// equal. Note: Due to floating-point precision errors, consider using
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