252 lines
7.1 KiB
C++
252 lines
7.1 KiB
C++
/* Copyright (C) 2009 Wildfire Games.
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* This file is part of 0 A.D.
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*
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* 0 A.D. is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 2 of the License, or
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* (at your option) any later version.
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*
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* 0 A.D. is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with 0 A.D. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "precompiled.h"
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#include "NUSpline.h"
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#include "Matrix3D.h"
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//Note: column major order! Each set of 4 constitutes a column.
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CMatrix3D HermiteSpline( 2.f, -3.f, 0.f, 1.f,
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-2.f, 3.f, 0.f, 0.f,
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1.f, -2.f, 1.f, 0.f,
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1.f, -1.f, 0.f, 0.f ); // Matrix H in article
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// cubic curve defined by 2 positions and 2 velocities
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CVector3D GetPositionOnCubic(const CVector3D &startPos, const CVector3D &startVel, const CVector3D &endPos, const CVector3D &endVel, float time)
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{
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CMatrix3D m( startPos.X, endPos.X, startVel.X, endVel.X,
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startPos.Y, endPos.Y, startVel.Y, endVel.Y,
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startPos.Z, endPos.Z, startVel.Z, endVel.Z,
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0.0f, 0.0f, 0.0f, 1.0f );
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m = m * HermiteSpline; // multiply by the mixer
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CVector3D TimeVector(time*time*time, time*time, time);
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CVector3D Result;
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m.Transform(TimeVector, Result);
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return Result;
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}
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/*********************************** R N S **************************************************/
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// adds node and updates segment length
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void RNSpline::AddNode(const CVector3D &pos)
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{
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if ( NodeCount >= MAX_SPLINE_NODES )
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return;
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if (NodeCount == 0)
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MaxDistance = 0.f;
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else
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{
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Node[NodeCount-1].Distance = (Node[NodeCount-1].Position - pos).Length();
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MaxDistance += Node[NodeCount-1].Distance;
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}
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SplineData temp;
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temp.Position = pos;
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Node.push_back(temp);
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NodeCount++;
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}
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// called after all nodes added. This function calculates the node velocities
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void RNSpline::BuildSpline()
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{
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if ( NodeCount == 2 )
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{
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Node[0].Velocity = GetStartVelocity(0);
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Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
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return;
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}
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else if ( NodeCount < 2 )
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return;
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for (int i = 1; i<NodeCount-1; i++)
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{
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CVector3D Next = Node[i+1].Position - Node[i].Position;
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CVector3D Previous = Node[i-1].Position - Node[i].Position;
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Next.Normalize();
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Previous.Normalize();
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// split the angle (figure 4)
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Node[i].Velocity = Next - Previous;
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Node[i].Velocity.Normalize();
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}
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// calculate start and end velocities
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Node[0].Velocity = GetStartVelocity(0);
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Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
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}
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// spline access function. time is 0 -> 1
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CVector3D RNSpline::GetPosition(float time) const
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{
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if ( NodeCount < 2 )
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return CVector3D(0.0f, 0.0f, 0.0f);
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if ( time > 1.0f )
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time = 1.0f;
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float Distance = time * MaxDistance;
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float CurrentDistance = 0.f;
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int i = 0;
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//Find which node we're on
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while (CurrentDistance + Node[i].Distance < Distance
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&& i < NodeCount - 2)
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{
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CurrentDistance += Node[i].Distance;
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i++;
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}
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debug_assert( i < NodeCount - 1 );
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float t = Distance - CurrentDistance;
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t /= Node[i].Distance; // scale t in range 0 - 1
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CVector3D startVel = Node[i].Velocity * Node[i].Distance;
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CVector3D endVel = Node[i+1].Velocity * Node[i].Distance;
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return GetPositionOnCubic(Node[i].Position, startVel,
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Node[i+1].Position, endVel, t);
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}
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// internal. Based on Equation 14
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CVector3D RNSpline::GetStartVelocity(int index)
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{
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if ( index >= NodeCount - 1 || index < 0)
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return CVector3D(0.0f, 0.0f, 0.0f);
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CVector3D temp = (Node[index+1].Position - Node[index].Position) * 3.0f * ( 1.0f / Node[index].Distance) ;
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return (temp - Node[index+1].Velocity)*0.5f;
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}
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// internal. Based on Equation 15
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CVector3D RNSpline::GetEndVelocity(int index)
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{
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if ( index >= NodeCount || index < 1)
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return CVector3D(0.0f, 0.0f, 0.0f);
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CVector3D temp = (Node[index].Position - Node[index-1].Position) * 3.0f * (1.0f / Node[index-1].Distance);
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return (temp - Node[index-1].Velocity) * 0.5f;
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}
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/*********************************** S N S **************************************************/
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// smoothing filter.
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void SNSpline::Smooth()
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{
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if ( NodeCount < 3 )
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return;
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CVector3D newVel;
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CVector3D oldVel = GetStartVelocity(0);
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for (int i = 1; i<NodeCount-1; i++)
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{
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// Equation 12
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newVel = GetEndVelocity(i) * Node[i].Distance +
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GetStartVelocity(i) * Node[i-1].Distance;
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newVel = newVel * ( 1 / (Node[i-1].Distance + Node[i].Distance) );
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Node[i-1].Velocity = oldVel;
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oldVel = newVel;
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}
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Node[NodeCount-1].Velocity = GetEndVelocity(NodeCount-1);
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Node[NodeCount-2].Velocity = oldVel;
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}
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/*********************************** T N S **************************************************/
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// as with RNSpline but use timePeriod in place of actual node spacing
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// ie time period is time from last node to this node
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void TNSpline::AddNode(const CVector3D &pos, const CVector3D& rotation, float timePeriod)
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{
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if ( NodeCount >= MAX_SPLINE_NODES )
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return;
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if (NodeCount == 0)
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MaxDistance = 0.f;
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else
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{
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Node[NodeCount-1].Distance = timePeriod;
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MaxDistance += Node[NodeCount-1].Distance;
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}
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SplineData temp;
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temp.Position = pos;
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//make sure we don't end up using undefined numbers...
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temp.Distance = 0.0f;
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temp.Velocity = CVector3D( 0.0f, 0.0f, 0.0f );
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temp.Rotation = rotation;
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Node.push_back(temp);
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NodeCount++;
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}
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//Inserts node before position
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void TNSpline::InsertNode(const int index, const CVector3D &pos, const CVector3D& rotation, float timePeriod)
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{
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if ( NodeCount >= MAX_SPLINE_NODES || index < NodeCount - 1 )
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return;
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if (NodeCount == 0)
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MaxDistance = 0.f;
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else
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{
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Node[NodeCount-1].Distance = timePeriod;
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Node[NodeCount-1].Rotation = rotation;
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MaxDistance += Node[NodeCount-1].Distance;
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}
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SplineData temp;
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temp.Position = pos;
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Node.insert(Node.begin() + index, temp);
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NodeCount++;
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}
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//Removes node at index
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void TNSpline::RemoveNode(const int index)
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{
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if (NodeCount == 0 || index > NodeCount - 1 )
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{
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return;
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}
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else
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{
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MaxDistance -= Node[index].Distance;
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MaxDistance -= Node[index-1].Distance;
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Node[index-1].Distance = 0.0f;
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Node.erase( Node.begin() + index, Node.begin() + index + 1 );
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}
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NodeCount--;
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}
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void TNSpline::UpdateNodeTime(const int index, float time)
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{
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if (NodeCount == 0 || index > NodeCount - 1 )
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{
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return;
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}
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Node[index].Distance = time;
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}
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void TNSpline::UpdateNodePos(const int index, const CVector3D &pos)
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{
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if (NodeCount == 0 || index > NodeCount - 1 )
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{
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return;
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}
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Node[index].Position = pos;
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}
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void TNSpline::Constrain()
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{
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if ( NodeCount < 3 )
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return;
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for (int i = 1; i<NodeCount-1; i++)
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{
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// Equation 13
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float r0 = (Node[i].Position-Node[i-1].Position).Length() / Node[i-1].Distance;
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float r1 = (Node[i+1].Position - Node[i].Position).Length() / Node[i].Distance;
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Node[i].Velocity *= 4.0f*r0*r1/((r0+r1)*(r0+r1));
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}
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}
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