FlaxEngine/Source/Engine/Core/Math/Transform.cpp

// Copyright (c) 2012-2024 Wojciech Figat. All rights reserved.

#include "Transform.h"
#include "Double4x4.h"
#include "Matrix.h"
#include "Matrix3x3.h"
#include "../Types/String.h"

Transform Transform::Identity(Vector3(0, 0, 0));

Transform::Transform(const Vector3& position, const Matrix3x3& rotationScale)
    : Translation(position)
{
    rotationScale.Decompose(Scale, Orientation);
}

String Transform::ToString() const
{
    return String::Format(TEXT("{}"), *this);
}

bool Transform::IsIdentity() const
{
    return Translation.IsZero() && Orientation.IsIdentity() && Scale.IsOne();
}

bool Transform::IsNanOrInfinity() const
{
    return Translation.IsNanOrInfinity() || Orientation.IsNanOrInfinity() || Scale.IsNanOrInfinity();
}

Matrix Transform::GetRotation() const
{
    Matrix result;
    Matrix::RotationQuaternion(Orientation, result);
    return result;
}

void Transform::GetRotation(Matrix& result) const
{
    Matrix::RotationQuaternion(Orientation, result);
}

void Transform::SetRotation(const Matrix& value)
{
    Quaternion::RotationMatrix(value, Orientation);
}

Matrix Transform::GetWorld() const
{
    Matrix result;
    Matrix::Transformation(Scale, Orientation, Translation, result);
    return result;
}

void Transform::GetWorld(Matrix& result) const
{
    Matrix::Transformation(Scale, Orientation, Translation, result);
}

void Transform::GetWorld(Double4x4& result) const
{
    Double4x4::Transformation(Scale, Orientation, Translation, result);
}

Transform Transform::Add(const Vector3& translation) const
{
    Transform result;
    result.Orientation = Orientation;
    result.Scale = Scale;
    Vector3::Add(Translation, translation, result.Translation);
    return result;
}

Transform Transform::Add(const Transform& other) const
{
    Transform result;
    Quaternion::Multiply(Orientation, other.Orientation, result.Orientation);
    result.Orientation.Normalize();
    Float3::Multiply(Scale, other.Scale, result.Scale);
    Vector3::Add(Translation, other.Translation, result.Translation);
    return result;
}

Transform Transform::Subtract(const Transform& other) const
{
    Transform result;
    Vector3::Subtract(Translation, other.Translation, result.Translation);
    const Quaternion invRotation = other.Orientation.Conjugated();
    Quaternion::Multiply(Orientation, invRotation, result.Orientation);
    result.Orientation.Normalize();
    Float3::Divide(Scale, other.Scale, result.Scale);
    return result;
}

void Transform::LocalToWorld(const Transform& other, Transform& result) const
{
    //Quaternion::Multiply(Orientation, other.Orientation, result.Orientation);
    const float a = Orientation.Y * other.Orientation.Z - Orientation.Z * other.Orientation.Y;
    const float b = Orientation.Z * other.Orientation.X - Orientation.X * other.Orientation.Z;
    const float c = Orientation.X * other.Orientation.Y - Orientation.Y * other.Orientation.X;
    const float d = Orientation.X * other.Orientation.X + Orientation.Y * other.Orientation.Y + Orientation.Z * other.Orientation.Z;
    result.Orientation.X = Orientation.X * other.Orientation.W + other.Orientation.X * Orientation.W + a;
    result.Orientation.Y = Orientation.Y * other.Orientation.W + other.Orientation.Y * Orientation.W + b;
    result.Orientation.Z = Orientation.Z * other.Orientation.W + other.Orientation.Z * Orientation.W + c;
    result.Orientation.W = Orientation.W * other.Orientation.W - d;

    //result.Orientation.Normalize();
    const float length = result.Orientation.Length();
    if (length > ZeroTolerance)
    {
        const float inv = 1.0f / length;
        result.Orientation.X *= inv;
        result.Orientation.Y *= inv;
        result.Orientation.Z *= inv;
        result.Orientation.W *= inv;
    }

    //Vector3::Multiply(Scale, other.Scale, result.Scale);
    result.Scale = Float3(Scale.X * other.Scale.X, Scale.Y * other.Scale.Y, Scale.Z * other.Scale.Z);

    //Vector3 tmp; Vector3::Multiply(other.Translation, Scale, tmp);
    Vector3 tmp = Vector3(other.Translation.X * Scale.X, other.Translation.Y * Scale.Y, other.Translation.Z * Scale.Z);

    //Vector3::Transform(tmp, Orientation, tmp);
    const float x = Orientation.X + Orientation.X;
    const float y = Orientation.Y + Orientation.Y;
    const float z = Orientation.Z + Orientation.Z;
    const float wx = Orientation.W * x;
    const float wy = Orientation.W * y;
    const float wz = Orientation.W * z;
    const float xx = Orientation.X * x;
    const float xy = Orientation.X * y;
    const float xz = Orientation.X * z;
    const float yy = Orientation.Y * y;
    const float yz = Orientation.Y * z;
    const float zz = Orientation.Z * z;
    tmp = Vector3(
        tmp.X * (1.0f - yy - zz) + tmp.Y * (xy - wz) + tmp.Z * (xz + wy),
        tmp.X * (xy + wz) + tmp.Y * (1.0f - xx - zz) + tmp.Z * (yz - wx),
        tmp.X * (xz - wy) + tmp.Y * (yz + wx) + tmp.Z * (1.0f - xx - yy));

    //Vector3::Add(tmp, Translation, result.Translation);
    result.Translation = Vector3(tmp.X + Translation.X, tmp.Y + Translation.Y, tmp.Z + Translation.Z);
}

void Transform::LocalToWorldVector(const Vector3& vector, Vector3& result) const
{
    Vector3 tmp = vector * Scale;
    Vector3::Transform(tmp, Orientation, result);
}

void Transform::LocalToWorld(const Vector3& point, Vector3& result) const
{
    Vector3 tmp = point * Scale;
    Vector3::Transform(tmp, Orientation, tmp);
    Vector3::Add(tmp, Translation, result);
}

void Transform::WorldToLocal(const Transform& other, Transform& result) const
{
    Vector3 invScale = Scale;
    if (invScale.X != 0.0f)
        invScale.X = 1.0f / invScale.X;
    if (invScale.Y != 0.0f)
        invScale.Y = 1.0f / invScale.Y;
    if (invScale.Z != 0.0f)
        invScale.Z = 1.0f / invScale.Z;
    const Quaternion invRotation = Orientation.Conjugated();
    Quaternion::Multiply(invRotation, other.Orientation, result.Orientation);
    result.Orientation.Normalize();
    Float3::Multiply(other.Scale, invScale, result.Scale);
    const Vector3 tmp = other.Translation - Translation;
    Vector3::Transform(tmp, invRotation, result.Translation);
    Vector3::Multiply(result.Translation, invScale, result.Translation);
}

void Transform::WorldToLocal(const Vector3& point, Vector3& result) const
{
    Vector3 invScale = Scale;
    if (invScale.X != 0.0f)
        invScale.X = 1.0f / invScale.X;
    if (invScale.Y != 0.0f)
        invScale.Y = 1.0f / invScale.Y;
    if (invScale.Z != 0.0f)
        invScale.Z = 1.0f / invScale.Z;
    const Quaternion invRotation = Orientation.Conjugated();
    result = point - Translation;
    Vector3::Transform(result, invRotation, result);
    result *= invScale;
}

void Transform::WorldToLocalVector(const Vector3& vector, Vector3& result) const
{
    Float3 invScale = Scale;
    if (invScale.X != 0.0f)
        invScale.X = 1.0f / invScale.X;
    if (invScale.Y != 0.0f)
        invScale.Y = 1.0f / invScale.Y;
    if (invScale.Z != 0.0f)
        invScale.Z = 1.0f / invScale.Z;
    const Quaternion invRotation = Orientation.Conjugated();
    Vector3::Transform(vector, invRotation, result);
    result *= invScale;
}

void Transform::WorldToLocal(const Quaternion& rotation, Quaternion& result) const
{
    Quaternion orientation = Orientation;
    orientation.Conjugate();
    Quaternion::Multiply(orientation, rotation, orientation);
    orientation.Normalize();
    result = orientation;
}

Float3 Transform::GetRight() const
{
    return Float3::Transform(Float3::Right, Orientation);
}

Float3 Transform::GetLeft() const
{
    return Float3::Transform(Float3::Left, Orientation);
}

Float3 Transform::GetUp() const
{
    return Float3::Transform(Float3::Up, Orientation);
}

Float3 Transform::GetDown() const
{
    return Float3::Transform(Float3::Down, Orientation);
}

Float3 Transform::GetForward() const
{
    return Float3::Transform(Float3::Forward, Orientation);
}

Float3 Transform::GetBackward() const
{
    return Float3::Transform(Float3::Backward, Orientation);
}

Transform Transform::Lerp(const Transform& t1, const Transform& t2, float amount)
{
    Transform result;
    Vector3::Lerp(t1.Translation, t2.Translation, amount, result.Translation);
    Quaternion::Slerp(t1.Orientation, t2.Orientation, amount, result.Orientation);
    Float3::Lerp(t1.Scale, t2.Scale, amount, result.Scale);
    return result;
}

void Transform::Lerp(const Transform& t1, const Transform& t2, float amount, Transform& result)
{
    Vector3::Lerp(t1.Translation, t2.Translation, amount, result.Translation);
    Quaternion::Slerp(t1.Orientation, t2.Orientation, amount, result.Orientation);
    Float3::Lerp(t1.Scale, t2.Scale, amount, result.Scale);
}

Transform Transform::AlignRotationToNormalAndSnapToGrid(const Vector3& point, const Vector3& normal, const Vector3& normalOffset, const Transform& relativeTo, const Vector3& gridSize, const Float3& scale)
{
    Quaternion rot = Quaternion::GetRotationFromNormal(normal, relativeTo);
    return Transform(Vector3::SnapToGrid(point, gridSize, rot, relativeTo.Translation, normalOffset), rot, scale);
}