0ad/source/maths/NUSpline.cpp

/* Copyright (C) 2015 Wildfire Games.
 * This file is part of 0 A.D.
 *
 * 0 A.D. is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 2 of the License, or
 * (at your option) any later version.
 *
 * 0 A.D. is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with 0 A.D.  If not, see <http://www.gnu.org/licenses/>.
 */

#include "precompiled.h"
#include "NUSpline.h"
#include "Matrix3D.h"

//Note: column major order!  Each set of 4 constitutes a column. 
CMatrix3D HermiteSpline(2.f, -3.f, 0.f, 1.f, 
                        -2.f, 3.f, 0.f, 0.f, 
                        1.f, -2.f, 1.f, 0.f, 
                        1.f, -1.f, 0.f, 0.f);  // Matrix H in article


// cubic curve defined by 2 positions and 2 velocities
CVector3D GetPositionOnCubic(const CVector3D& startPos, const CVector3D& startVel, const CVector3D& endPos, const CVector3D& endVel, float time)
{
	CMatrix3D m(startPos.X, endPos.X, startVel.X, endVel.X, 
	            startPos.Y, endPos.Y, startVel.Y, endVel.Y,
	            startPos.Z, endPos.Z, startVel.Z, endVel.Z, 
	            0.0f, 0.0f, 0.0f, 1.0f);

	m = m * HermiteSpline; // multiply by the mixer

	CVector3D TimeVector(time*time*time, time*time, time);
	CVector3D Result;
	m.Transform(TimeVector, Result);
	return Result;
}

/*********************************** R N S **************************************************/

// adds node and updates segment length
void RNSpline::AddNode(const CFixedVector3D& pos)
{
	if (NodeCount >= MAX_SPLINE_NODES)
		return;
	if (NodeCount == 0)
		MaxDistance = fixed::Zero();
	else
	{
		Node[NodeCount-1].Distance = (Node[NodeCount-1].Position - pos).Length();
		MaxDistance += Node[NodeCount-1].Distance;
	}
	SplineData temp;
	temp.Position = pos;
	Node.push_back(temp);
	++NodeCount;
}


// called after all nodes added. This function calculates the node velocities
void RNSpline::BuildSpline()
{
	if (NodeCount == 2)
	{
		Node[0].Velocity = GetStartVelocity(0);
		Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
		return;
	}
	else if (NodeCount < 2)
		return;

	for (int i = 1; i < NodeCount-1; ++i)
	{
		CVector3D Next = Node[i+1].Position - Node[i].Position;
		CVector3D Previous = Node[i-1].Position - Node[i].Position;
		Next.Normalize();
		Previous.Normalize();

		// split the angle (figure 4)
		Node[i].Velocity = Next - Previous;
		Node[i].Velocity.Normalize();
	}
	// calculate start and end velocities
	Node[0].Velocity = GetStartVelocity(0);
	Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
}

// spline access function. time is 0 -> 1
CVector3D RNSpline::GetPosition(float time) const
{
	if (NodeCount < 2)
		return CVector3D(0.0f, 0.0f, 0.0f);
	if (time < 0.0f)
		time = 0.0f;
	if (time > 1.0f)
		time = 1.0f;
	float Distance = time * MaxDistance.ToFloat();
	float CurrentDistance = 0.f;
	int i = 0;

	// Find which node we're on
	while (CurrentDistance + Node[i].Distance.ToFloat() < Distance && i < NodeCount - 2)
	{
		CurrentDistance += Node[i].Distance.ToFloat();
		++i;
	}
	ENSURE(i < NodeCount - 1);
	float t = Distance - CurrentDistance;
	// TODO: reimplement CVector3D comparator (float comparing is bad without EPS)
	if (Node[i].Position == Node[i+1].Position || Node[i].Distance.ToFloat() < 1e-7) // distance too small or zero
	{
		return Node[i+1].Position;
	}
	t /= Node[i].Distance.ToFloat(); // scale t in range 0 - 1
	CVector3D startVel = Node[i].Velocity * Node[i].Distance.ToFloat();
	CVector3D endVel = Node[i+1].Velocity * Node[i].Distance.ToFloat();
	return GetPositionOnCubic(Node[i].Position, startVel,
		Node[i+1].Position, endVel, t);
}

// internal. Based on Equation 14 
CVector3D RNSpline::GetStartVelocity(int index)
{
	if (index >= NodeCount - 1 || index < 0)
		return CVector3D(0.0f, 0.0f, 0.0f);
	CVector3D temp = CVector3D(Node[index+1].Position - Node[index].Position) * 3.0f * (1.0f / Node[index].Distance.ToFloat());
	return (temp - Node[index+1].Velocity)*0.5f;
}

// internal. Based on Equation 15 
CVector3D RNSpline::GetEndVelocity(int index)
{
	if (index >= NodeCount || index < 1)
		return CVector3D(0.0f, 0.0f, 0.0f);
	CVector3D temp = CVector3D(Node[index].Position - Node[index-1].Position) * 3.0f * (1.0f / Node[index-1].Distance.ToFloat());
	return (temp - Node[index-1].Velocity) * 0.5f;
}

/*********************************** S N S **************************************************/

// smoothing filter.
void SNSpline::Smooth()
{
	if (NodeCount < 3)
		return;

	CVector3D newVel;
	CVector3D oldVel = GetStartVelocity(0);
	for (int i = 1; i < NodeCount-1; ++i)
	{
		// Equation 12
		newVel = GetEndVelocity(i) * Node[i].Distance.ToFloat() + GetStartVelocity(i) * Node[i-1].Distance.ToFloat();
		newVel = newVel * (1 / (Node[i-1].Distance + Node[i].Distance).ToFloat());
		Node[i-1].Velocity = oldVel;
		oldVel = newVel;
	}
	Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
	Node[NodeCount-2].Velocity = oldVel;
}

/*********************************** T N S **************************************************/

// as with RNSpline but use timePeriod in place of actual node spacing
// ie time period is time from last node to this node
void TNSpline::AddNode(const CFixedVector3D& pos, const CFixedVector3D& rotation, fixed timePeriod)
{
	if (NodeCount >= MAX_SPLINE_NODES)
		return;

	if (NodeCount == 0)
		MaxDistance = fixed::Zero();
	else
	{
		Node[NodeCount-1].Distance = timePeriod;
		MaxDistance += Node[NodeCount-1].Distance;
	}

	SplineData temp;
	temp.Position = pos;

	//make sure we don't end up using undefined numbers...
	temp.Distance = fixed::Zero();
	temp.Velocity = CVector3D(0.0f, 0.0f, 0.0f);
	temp.Rotation = rotation;
	Node.push_back(temp);
	++NodeCount;
}

//Inserts node before position
void TNSpline::InsertNode(const int index, const CFixedVector3D& pos, const CFixedVector3D& rotation, fixed timePeriod)
{
	if (NodeCount >= MAX_SPLINE_NODES || index < NodeCount - 1)
		return;
	if (NodeCount == 0)
		MaxDistance = fixed::Zero();
	else
	{
		Node[NodeCount-1].Distance = timePeriod;
		Node[NodeCount-1].Rotation = rotation;
		MaxDistance += Node[NodeCount-1].Distance;
	}
	SplineData temp;
	temp.Position = pos;
	Node.insert(Node.begin() + index, temp);
	++NodeCount;
}

//Removes node at index
void TNSpline::RemoveNode(const int index)
{
	if (NodeCount == 0 || index > NodeCount - 1)
		return;

	MaxDistance -= Node[index].Distance;
	MaxDistance -= Node[index-1].Distance;
	Node[index-1].Distance = fixed::Zero();
	Node.erase(Node.begin() + index, Node.begin() + index + 1);
	--NodeCount;
}
void TNSpline::UpdateNodeTime(const int index, fixed time)
{
	if (NodeCount == 0 || index > NodeCount - 1)
		return;

	Node[index].Distance = time;
}
void TNSpline::UpdateNodePos(const int index, const CFixedVector3D& pos)
{
	if (NodeCount == 0 || index > NodeCount - 1)
		return;

	Node[index].Position = pos;
}

void TNSpline::Constrain()
{
	if (NodeCount < 3)
		return;

	for (int i = 1; i < NodeCount-1; ++i)
	{
		// Equation 13
		float r0 = (Node[i].Position - Node[i - 1].Position).Length().ToFloat() / Node[i-1].Distance.ToFloat();
		float r1 = (Node[i+1].Position - Node[i].Position).Length().ToFloat() / Node[i].Distance.ToFloat();
		Node[i].Velocity *= 4.0f*r0*r1 / ((r0 + r1)*(r0 + r1));
	}
}