/// <summary> /// Gets both the position and the first derivative of position /// at time ti. The time is clamped within the t0 - t1 range. /// </summary> public void PositionAndVelAt(float t, out __CHS_T__ position, out __CHS_T__ velocity) { float C00 = t1 - t0; float C1 = 1.0f / C00; float i, i2, i3; float i_, i2_, i3_; { i = Mathf.Clamp01((t - t0) * C1); i_ = C1; i2 = i * i; i2_ = 2 * i * i_; i3 = i2 * i; i3_ = i2_ * i + i_ * i2; } __CHS_T__ h00 = (2 * i3 - 3 * i2 + 1) * pos0; __CHS_T__ h00_ = (i3_ * 2 - i2_ * 3) * pos0; __CHS_T__ h10 = (i3 - 2 * i2 + i) * C00 * vel0; __CHS_T__ h10_ = (i3_ - 2 * i2_ + i_) * C00 * vel0; __CHS_T__ h01 = (3 * i2 - 2 * i3) * pos1; __CHS_T__ h01_ = (i2_ * 3 - 2 * i3_) * pos1; __CHS_T__ h11 = (i3 - i2) * C00 * vel1; __CHS_T__ h11_ = (i3_ - i2_) * C00 * vel1; position = h00 + h01 + h10 + h11; velocity = h00_ + h01_ + h10_ + h11_; }
/// <summary> /// Constructs a spline by specifying the positions, /// velocities, and times of the endpoints. /// </summary> public __CHS__(float t0, float t1, __CHS_T__ pos0, __CHS_T__ pos1, __CHS_T__ vel0, __CHS_T__ vel1) { this.t0 = t0; this.t1 = t1; this.vel0 = vel0; this.vel1 = vel1; this.pos0 = pos0; this.pos1 = pos1; }
/// <summary> /// Constructs a spline by specifying the positions and /// velocities of the two endpoints. The time range of /// the spline is 0 to length. /// </summary> public __CHS__(__CHS_T__ pos0, __CHS_T__ pos1, __CHS_T__ vel0, __CHS_T__ vel1, float length) { t0 = 0; t1 = length; this.vel0 = vel0; this.vel1 = vel1; this.pos0 = pos0; this.pos1 = pos1; }
/// <summary> /// Constructs a spline by specifying the positions and /// velocities of the two endpoints. The time range of /// the spline is 0 to 1. /// </summary> public __CHS__(__CHS_T__ pos0, __CHS_T__ pos1, __CHS_T__ vel0, __CHS_T__ vel1) { t0 = 0; t1 = 1; this.vel0 = vel0; this.vel1 = vel1; this.pos0 = pos0; this.pos1 = pos1; }
/// <summary> /// Constructs a spline by specifying the positions of the /// two endpoints. The velocity at each endpoint is zero, /// and the time range of the spline is 0 to 1. /// </summary> public __CHS__(__CHS_T__ pos0, __CHS_T__ pos1) { t0 = 0; t1 = 1; vel0 = default(__CHS_T__); vel1 = default(__CHS_T__); this.pos0 = pos0; this.pos1 = pos1; }
/// <summary> /// Gets the position at time t along this spline. /// The time is clamped within the t0 - t1 range. /// </summary> public __CHS_T__ PositionAt(float t) { float i = Mathf.Clamp01((t - t0) / (t1 - t0)); float i2 = i * i; float i3 = i2 * i; __CHS_T__ h00 = (2 * i3 - 3 * i2 + 1) * pos0; __CHS_T__ h10 = (i3 - 2 * i2 + i) * (t1 - t0) * vel0; __CHS_T__ h01 = (-2 * i3 + 3 * i2) * pos1; __CHS_T__ h11 = (i3 - i2) * (t1 - t0) * vel1; return(h00 + h10 + h01 + h11); }
/// <summary> /// Gets the first derivative of position at time t. /// The time is clamped within the t0 - t1 range. /// </summary> public __CHS_T__ VelocityAt(float t) { float C00 = t1 - t0; float C1 = 1.0f / C00; float i, i2; float i_, i2_, i3_; { i = Mathf.Clamp01((t - t0) * C1); i_ = C1; i2 = i * i; i2_ = 2 * i * i_; i3_ = i2_ * i + i_ * i2; } __CHS_T__ h00_ = (i3_ * 2 - i2_ * 3) * pos0; __CHS_T__ h10_ = (i3_ - 2 * i2_ + i_) * C00 * vel0; __CHS_T__ h01_ = (i2_ * 3 - 2 * i3_) * pos1; __CHS_T__ h11_ = (i3_ - i2_) * C00 * vel1; return(h00_ + h01_ + h10_ + h11_); }