public override void Update(GameTime gameTime)
{
// Update _time.
_time += (float)gameTime.ElapsedGameTime.TotalSeconds;
var debugRenderer = GraphicsScreen.DebugRenderer;
debugRenderer.Clear();
// Draw the path key points.
foreach (var point in _path.Select(key => key.Point))
{
debugRenderer.DrawPoint(point, Color.Black, false);
}
// Draw the path.
for (float i = 0; i < _path.Last().Parameter; i += 0.1f)
{
var point0 = _path.GetPoint(i);
var point1 = _path.GetPoint((i + 0.1f));
debugRenderer.DrawLine(point0, point1, Color.Black, false);
}
// Move an object with constant speed along the path.
const float speed = 2;
var traveledDistance = _time * speed;
// Get path parameter where the path length is equal to traveledDistance.
var parameter = _path.GetParameterFromLength(traveledDistance, 10, 0.01f);
// Get path point at the traveledDistance.
Vector3F position = _path.GetPoint(parameter);
// Get the path tangent at traveledDistance and use it as the forward direction.
Vector3F forward = _path.GetTangent(parameter).Normalized;
// Draw an object on the path.
DrawObject(position, forward);
base.Update(gameTime);
}
public override void Update(GameTime gameTime)
{
float deltaTime = (float)gameTime.ElapsedGameTime.TotalSeconds;
// Move an object with constant speed along the path.
const float speed = 5;
float newPathPosition = _currentPathPosition + deltaTime * speed;
// Get path parameter where the path length is equal to newPathPosition.
float parameter = _path.GetParameterFromLength(newPathPosition, 10, 0.01f);
// Get path point at the newPathPosition.
Vector3 position = _path.GetPoint(parameter);
// Get the path tangent at newPathPosition and use it as the forward direction.
Vector3 forward = _path.GetTangent(parameter).Normalized;
Quaternion currentOrientation = Quaternion.CreateFromRotationMatrix(_kinematicBody.Pose.Orientation);
Quaternion targetOrientation = Quaternion.CreateFromRotationMatrix(Vector3.UnitY, forward);
Quaternion orientationDelta = targetOrientation * currentOrientation.Conjugated;
// Selective Negation:
// A certain rotation can be described by two quaternions: q and -q. For example, if you look
// to the north and want to look to the east you can either rotate 90 degrees clockwise or
// 270 degrees counter-clockwise. In the game we always want to rotate using the
// smaller angle. This is done using "Selective Negation": The dot product of two quaternions
// is proportional to the cosine of the rotation angle. If the cosine of the angle is < 0,
// the angle is larger than +/- 90 degrees. In this case we must use -orientationDelta to
// rotate using the smaller angle.
if (Quaternion.Dot(currentOrientation, targetOrientation) < 0)
{
orientationDelta = -orientationDelta;
}
// We could directly set the new position of the kinematic body. However, directly
// setting a position is like "teleporting" an object. The body would not interact
// properly with other objects in the physics simulation.
// Instead we apply a linear and angular velocity to the body. The simulation will
// automatically update the position of the body. If the body touches other objects
// along the way it will push these objects with the appropriate force.
// Note that the physics simulation may advance with a different time step than the
// rest of the game.
deltaTime = Math.Max(deltaTime, Simulation.Settings.Timing.FixedTimeStep);
// Determine the linear velocity that moves the body forward.
Vector3 linearVelocity = (position - _kinematicBody.Pose.Position) / deltaTime;
// Determine the angular velocity that rotates the body.
Vector3 angularVelocity;
Vector3 rotationAxis = orientationDelta.Axis;
if (!rotationAxis.IsNumericallyZero)
{
// The angular velocity is computed as rotationAxis * rotationSpeed.
// The rotation speed is computed as angle / time. (Note: The angle is given in radians.)
float rotationSpeed = (orientationDelta.Angle / deltaTime);
angularVelocity = rotationAxis * rotationSpeed;
}
else
{
// The axis of rotation is 0. That means the no rotation should be applied.
angularVelocity = Vector3.Zero;
}
_kinematicBody.LinearVelocity = linearVelocity;
_kinematicBody.AngularVelocity = angularVelocity;
_currentPathPosition = newPathPosition;
// Let the base class render the rigid bodies.
base.Update(gameTime);
// Draw the 3D path.
var debugRenderer = GraphicsScreen.DebugRenderer;
for (int i = 0; i < _pointList.Length; i++)
{
debugRenderer.DrawLine(_pointList[i], _pointList[(i + 1) % _pointList.Length], Color.Black, false);
}
}
public void TwoKeyCurvesTest()
{
Path3F curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.CatmullRom,
});
curve.Add(new PathKey3F()
{
Parameter = 3,
Point = new Vector3F(3, 4, 0),
Interpolation = SplineInterpolation.CatmullRom,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(2, 3, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(3, 4, 0), curve.GetPoint(3));
Assert.AreEqual(new Vector3F(3, 4, 0), curve.GetPoint(4));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(1, 1, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(1, 1, 0), curve.GetTangent(2));
Assert.AreEqual(new Vector3F(1, 1, 0), curve.GetTangent(3));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(4));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(2, 2, 0).Length, curve.GetLength(0, 4, 10, 0.01f), 0.01f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
}
public void OneKeyCurvesTest()
{
// Test linear curves with 1 point
Path3F curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.Linear,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
// Test step curves with 1 point
curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.StepLeft,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
// Test B-spline curves with 1 point
curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.BSpline,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
// Test Catmull-Rom curves with 1 point
curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.CatmullRom,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
// Test Hermite curves with 1 point
curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector3F(2, -2, 0),
TangentOut = new Vector3F(2, 2, 0),
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 20, 0.01f));
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(3, 4, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(2, 2, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(2, 2, 0), curve.GetTangent(2));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(2, 2, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(-1, 4, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(2, -2, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(2, -2, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(2, 2, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(-1, 4, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(3, 4, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(2, -2, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(2, 2, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(2, 2, 0), curve.GetTangent(2));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(4, 4, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
// Test Bezier curves with 1 point
curve = new Path3F();
curve.Add(new PathKey3F()
{
Parameter = 1,
Point = new Vector3F(1, 2, 0),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector3F(1, 2, 0) - new Vector3F(2, -2, 0) / 3,
TangentOut = new Vector3F(1, 2, 0) + new Vector3F(2, 2, 0) / 3,
});
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(3, 4, 0), curve.GetPoint(2)));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, 2, 0), curve.GetTangent(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, 2, 0), curve.GetTangent(2)));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(2, 2, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Constant;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(-1, 4, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, -2, 0), curve.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, -2, 0), curve.GetTangent(1)));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(2, 2, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(-1, 4, 0), curve.GetPoint(0));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(3, 4, 0), curve.GetPoint(2)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, -2, 0), curve.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, 2, 0), curve.GetTangent(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(2, 2, 0), curve.GetTangent(2)));
Assert.IsTrue(Numeric.AreEqual(new Vector3F(4, 4, 0).Length, curve.GetLength(0, 2, 10, 0.01f), 0.1f));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.Cycle;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
curve.PreLoop = CurveLoopType.Oscillate;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(1));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(0));
Assert.AreEqual(new Vector3F(1, 2, 0), curve.GetPoint(2));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(0));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(1));
Assert.AreEqual(new Vector3F(0, 0, 0), curve.GetTangent(2));
Assert.AreEqual(0, curve.GetLength(0, 2, 10, 0.01f));
}
public void GetTangentShouldReturnZeroIfPathIsEmpty()
{
Path3F empty = new Path3F();
empty.Sort();
Assert.AreEqual(Vector3F.Zero, empty.GetTangent(-0.5f));
Assert.AreEqual(Vector3F.Zero, empty.GetTangent(0));
Assert.AreEqual(Vector3F.Zero, empty.GetTangent(0.5f));
}
public void GetTangent()
{
Path3F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(-10)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(10)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(11.5f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(16)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(85)));
CatmullRomSegment3F catmullOscillate = new CatmullRomSegment3F()
{
Point1 = new Vector3F(10, 12, 14),
Point2 = new Vector3F(10, 14, 8),
Point3 = new Vector3F(20, 14, 8),
Point4 = new Vector3F(30, 14, 8),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(43)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(-catmullOscillate.GetTangent(0.7f) / 10.0f, path.GetTangent(53)));
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(0)));
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(-36)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(4)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(83)));
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(1f) / 10.0f, path.GetTangent(434)));
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
path = new Path3F();
path.Add(new PathKey3F()
{
Parameter = 25,
Point = new Vector3F(6, 7, 14),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector3F(5, 6, 13),
TangentOut = new Vector3F(7, 8, 15),
});
path.Add(new PathKey3F()
{
Parameter = 35,
Point = new Vector3F(10, 12, 14),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector3F(1, 0, 0),
TangentOut = new Vector3F(1, 0, 0),
});
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Linear;
float Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(6, 7, 14) - new Vector3F(5, 6, 13)) * 3 / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(1, 0, 0) / Δu, path.GetTangent(100)));
path[1].Parameter = 25;
path[0].Parameter = 35;
path.Sort();
Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(1, 0, 0) / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(7, 8, 15) - new Vector3F(6, 7, 14)) * 3 / Δu, path.GetTangent(100)));
path.Add(new PathKey3F()
{
Parameter = 15,
Point = new Vector3F(0, 0, 0),
Interpolation = SplineInterpolation.BSpline,
});
path.Sort();
}