Finished quaternion implementation

SHADE_Engine/src/Math/SHQuaternion.cpp

@@ -211,15 +211,6 @@ namespace SHADE
     return XMVectorGetX(XMQuaternionDot(*this, rhs));
   }
 
-  SHQuaternion SHQuaternion::RotateTowards(const SHQuaternion&, float) const noexcept
-  {
-    SHQuaternion result;
-
-    // TODO (Diren)
-
-    return result;
-  }
-
   SHVec3 SHQuaternion::ToEuler() const noexcept
   {
     const float XX = x * x;
@@ -317,19 +308,32 @@ namespace SHADE
   }
 
 
-  float SHQuaternion::Angle(const SHQuaternion&, const SHQuaternion&) noexcept
+  float SHQuaternion::Angle(const SHQuaternion& q1, const SHQuaternion& q2) noexcept
   {
-    // TODO (Diren)
+    XMVECTOR R = XMQuaternionMultiply(XMQuaternionConjugate(q1), q2);
 
-    return 0.0f;
+    const float RS = XMVectorGetW(R);
+    R = XMVector3Length(R);
+    return 2.0f * atan2f(XMVectorGetX(R), RS);
   }
 
-  SHQuaternion SHQuaternion::Lerp(const SHQuaternion&, const SHQuaternion&, float) noexcept
+  SHQuaternion SHQuaternion::Lerp(const SHQuaternion& q1, const SHQuaternion& q2, float t) noexcept
   {
     SHQuaternion result;
 
-    // TODO (Diren)
+    XMVECTOR R = XMVectorZero();
+    if (XMVector4GreaterOrEqual(XMVector4Dot(q1, q2), R))
+    {
+      R = XMVectorLerp(q1, q2, t);
+    }
+    else
+    {
+      const XMVECTOR X0 = XMVectorMultiply(q1, XMVectorReplicate(1.f - t));
+      const XMVECTOR X1 = XMVectorMultiply(q2, XMVectorReplicate(t));
+      R = XMVectorSubtract(X0, X1);
+    }
 
+    XMStoreFloat4(&result, XMQuaternionNormalize(R));
     return result;
   }
 
@@ -341,13 +345,102 @@ namespace SHADE
     return result;
   }
 
-  SHQuaternion SHQuaternion::Rotate(const SHVec3& , const SHVec3&) noexcept
+  SHQuaternion SHQuaternion::ClampedLerp(const SHQuaternion& q1, const SHQuaternion& q2, float t, float tMin, float tMax) noexcept
   {
+    return Lerp(q1, q2, std::clamp(t, tMin, tMax));
+  }
+
+
+  SHQuaternion SHQuaternion::ClampedSlerp(const SHQuaternion& q1, const SHQuaternion& q2, float t, float tMin, float tMax) noexcept
+  {
+    return Slerp(q1, q2, std::clamp(t, tMin, tMax));
+  }
+
+  SHQuaternion SHQuaternion::FromToRotation(const SHVec3& from, const SHVec3& to) noexcept
+  {
+    // Melax, "The Shortest Arc Quaternion", Game Programming Gems
+
     SHQuaternion result;
 
-    // TODO (Diren)
+    const XMVECTOR F = XMVector3Normalize(from);
+    const XMVECTOR T = XMVector3Normalize(to);
+
+    const float dot = XMVectorGetX(XMVector3Dot(F, T));
+    if (dot >= 1.f)
+    {
+        result = Identity;
+    }
+    else if (dot <= -1.f)
+    {
+        XMVECTOR axis = XMVector3Cross(F, SHVec3::Right);
+        if (XMVector3NearEqual(XMVector3LengthSq(axis), g_XMZero, g_XMEpsilon))
+        {
+            axis = XMVector3Cross(F, SHVec3::Up);
+        }
+
+        const XMVECTOR Q = XMQuaternionRotationAxis(axis, XM_PI);
+        XMStoreFloat4(&result, Q);
+    }
+    else
+    {
+        const XMVECTOR C = XMVector3Cross(F, T);
+        XMStoreFloat4(&result, C);
+
+        const float s = sqrtf((1.f + dot) * 2.f);
+        result.x /= s;
+        result.y /= s;
+        result.z /= s;
+        result.w = s * 0.5f;
+    }
 
     return result;
   }
 
+  SHQuaternion SHQuaternion::LookRotation(const SHVec3& forward, const SHVec3& up) noexcept
+  {
+    SHQuaternion result;
+
+    const SHQuaternion Q1 = FromToRotation(SHVec3::Forward, forward);
+
+    const XMVECTOR C = XMVector3Cross(forward, up);
+    if (XMVector3NearEqual(XMVector3LengthSq(C), g_XMZero, g_XMEpsilon))
+    {
+        // forward and up are co-linear
+        return Q1;
+    }
+
+    SHVec3 qU;
+    XMStoreFloat3(&qU, XMQuaternionMultiply(Q1, SHVec3::Up));
+
+    const SHQuaternion Q2 = FromToRotation(qU, up);
+
+    XMStoreFloat4(&result, XMQuaternionMultiply(Q2, Q1));
+
+    return result;
+  }
+
+  SHQuaternion SHQuaternion::RotateTowards(const SHQuaternion& from, const SHQuaternion& to, float maxAngleInRad) noexcept
+  {
+    SHQuaternion result;
+
+    // We can use the conjugate here instead of inverse assuming q1 & q2 are normalized.
+    const XMVECTOR R = XMQuaternionMultiply(XMQuaternionConjugate(from), to);
+
+    const float RS = XMVectorGetW(R);
+    const XMVECTOR L = XMVector3Length(R);
+    const float angle = 2.f * atan2f(XMVectorGetX(L), RS);
+    if (angle > maxAngleInRad)
+    {
+        const XMVECTOR delta = XMQuaternionRotationAxis(R, maxAngleInRad);
+        const XMVECTOR Q = XMQuaternionMultiply(delta, from);
+        XMStoreFloat4(&result, Q);
+    }
+    else
+    {
+        // Don't overshoot.
+        result = to;
+    }
+    return result;
+  }
+
 } // namespace SHADE

SHADE_Engine/src/Math/SHQuaternion.h

@@ -51,7 +51,6 @@ namespace SHADE
     SHQuaternion  ()                                            noexcept;
     SHQuaternion  (const SHVec4& vec4)                          noexcept;
     SHQuaternion  (float x, float y, float z, float w)          noexcept;
-    SHQuaternion  (float yaw, float pitch, float roll)          noexcept;
 
     // Conversion from other math types
 
@@ -103,7 +102,6 @@ namespace SHADE
     [[nodiscard]] float         Length        ()  const noexcept;
     [[nodiscard]] float         LengthSquared ()  const noexcept;
     [[nodiscard]] float         Dot           (const SHQuaternion& rhs) const noexcept;
-    [[nodiscard]] SHQuaternion  RotateTowards (const SHQuaternion& target, float maxAngleInRad) const noexcept;
 
     [[nodiscard]] SHVec3        ToEuler       ()  const noexcept;
     [[nodiscard]] std::string   ToString      ()  const noexcept;
@@ -124,8 +122,12 @@ namespace SHADE
 
     [[nodiscard]] static SHQuaternion Lerp              (const SHQuaternion& q1, const SHQuaternion& q2, float t) noexcept;
     [[nodiscard]] static SHQuaternion Slerp             (const SHQuaternion& q1, const SHQuaternion& q2, float t) noexcept;
+    [[nodiscard]] static SHQuaternion ClampedLerp       (const SHQuaternion& q1, const SHQuaternion& q2, float t, float tMin = 0.0f, float tMax = 1.0f) noexcept;
+    [[nodiscard]] static SHQuaternion ClampedSlerp      (const SHQuaternion& q1, const SHQuaternion& q2, float t, float tMin = 0.0f, float tMax = 1.0f) noexcept;
 
-    [[nodiscard]] static SHQuaternion Rotate    (const SHVec3& from, const SHVec3& to)                    noexcept;
+    [[nodiscard]] static SHQuaternion FromToRotation  (const SHVec3& from, const SHVec3& to)    noexcept;
+    [[nodiscard]] static SHQuaternion LookRotation    (const SHVec3& forward, const SHVec3& up) noexcept;
+    [[nodiscard]] static SHQuaternion RotateTowards   (const SHQuaternion& from, const SHQuaternion& to, float maxAngleInRad) noexcept;
   };
 
   SHQuaternion operator*(float lhs, const SHQuaternion& rhs) noexcept;

SHADE_Managed/Quaternion.hxx

@@ -0,0 +1,17 @@
+/************************************************************************************//*!
+\file           Quaternion.hxx
+\author         Diren D Bharwani, diren.dbharwani, 390002520
+\par            email: diren.dbharwani\@digipen.edu
+\date           Oct 23, 2022
+\brief          Contains the definitions of Quaternion struct.
+ 
+                Note: This file is written in C++17/CLI.
+
+Copyright (C) 2021 DigiPen Institute of Technology.
+Reproduction or disclosure of this file or its contents without the prior written consent 
+of DigiPen Institute of Technology is prohibited.
+*//*************************************************************************************/
+
+#pragma once
+
+// TODO(Diren)

SHADE_Managed/src/Math/Vector3.hxx

@@ -11,6 +11,7 @@ Copyright (C) 2021 DigiPen Institute of Technology.
 Reproduction or disclosure of this file or its contents without the prior written consent 
 of DigiPen Institute of Technology is prohibited.
 *//*************************************************************************************/
+
 #pragma once
 
 // Standard Libraries