Unity實現汽車前後輪倒車軌跡計算

///<summary>
/// 獲取行車軌跡預測index = 0 left軌跡
/// </summary>
/// <param name="steeringAngle">方向盤角度</param>
/// <param name="carWheelbase">汽車前後軸距</param>
/// <param name="carWidth">車寬</param>
/// <param name="length">點位密度</param>
/// <param name="isFront">是否是前輪</param>
/// <param name="maxAngle">軌跡的最大轉彎角度</param>
/// <returns>交叉數組,下標為0的是右邊線, 下表為1的是左邊線</returns>
public Vector3[][] GetCarTrack(float steeringAngle, float carWheelbase, float carWidth, float length, bool isFront, float maxAngle = 90f)
        {
            float maxSteerAngle = _carControl._vehicleController.steering.maxSteerAngle;
            float theta = Mathf.Abs(steeringAngle / 180 * Mathf.PI);
            Vector3[][] track = new Vector3[2][];
            List<Vector3> trackLeft = new List<Vector3>();
            List<Vector3> trackRight = new List<Vector3>();
            if (theta == 0)
            {
                for (float i = 0; i < length; i++)
                {
                    float x = i / length * 5;
                    if (isFront)
                    {
                        x *= 1;
                        trackLeft.Add(new Vector3(x, 0f, carWidth));
                        trackRight.Add(new Vector3(x, 0f, 0f));
                    }
                    else
                    {
                        x *= -1;
                        trackLeft.Add(new Vector3(x, 0, carWidth));
                        trackRight.Add(new Vector3(x, 0, 0));
                    }
                }
            }
            else
            {
                if (isFront)
                {
                    float r = (carWheelbase / Mathf.Tan(theta) + carWidth / 2) / Mathf.Cos(theta);
                    float rMin = Mathf.Cos(theta) * r - carWidth;
                    float theta1 = Mathf.Atan(carWheelbase / rMin);
                    rMin = rMin / Mathf.Cos(theta1);
                    float rMax = rMin + carWidth;
                    float lineAngle = carWheelbase / (rMax * 2f * Mathf.PI) * 360f;
                    
                    for (int i = 0; i <= length; i++)
                    {
                        if (i / length >= (maxAngle - lineAngle) / maxAngle)
                        {
                            float x = rMin * Mathf.Cos(maxAngle / length * i * Mathf.Deg2Rad);
                            float z = rMin * Mathf.Sin(maxAngle / length * i * Mathf.Deg2Rad);
                            if (x >= carWheelbase)
                            {
                                if (steeringAngle > 0)
                                {
                                    trackRight.Add(new Vector3(x - carWheelbase, 0, z - rMin + steeringAngle / maxSteerAngle * (carWidth / 2)));
                                }
                                else
                                {
                                    trackRight.Add(new Vector3(x - carWheelbase, 0, -(z - rMin) + carWidth + steeringAngle / maxSteerAngle * (carWidth / 2)));
                                }
                            }

                            x = rMax * Mathf.Cos(maxAngle / length * i * Mathf.Deg2Rad);
                            z = rMax * Mathf.Sin(maxAngle / length * i * Mathf.Deg2Rad);
                            if (x >= carWheelbase)
                            {
                                if (steeringAngle > 0)
                                {
                                    trackLeft.Add(new Vector3(x - carWheelbase, 0, z - rMin + steeringAngle / maxSteerAngle * (carWidth / 2)));
                                }
                                else
                                {
                                    trackLeft.Add(new Vector3(x - carWheelbase, 0, -(z - rMin) + carWidth + steeringAngle / maxSteerAngle * (carWidth / 2)));
                                }
                            }
                        }
                    }
                    trackRight[trackRight.Count - 1] = Vector3.forward * trackRight[trackRight.Count - 1].z;
                    trackLeft[trackLeft.Count - 1] = Vector3.forward * trackLeft[trackLeft.Count - 1].z;
                }
                else
                {
                    float r = (carWheelbase / Mathf.Tan(theta) + carWidth / 2) / Mathf.Cos(theta);
                    float rMin = Mathf.Cos(theta) * r - carWidth;
                    float rMax = rMin + carWidth;
                    float lineAngle = carWheelbase / (rMin * 2f * Mathf.PI) * 360f;
                    for (int i = 0; i <= length; i++)
                    {
                        if (i / length >= (maxAngle - lineAngle) / maxAngle)
                        {
                            float x = -rMin * Mathf.Cos(maxAngle / length * i * Mathf.Deg2Rad);
                            float z = rMin * Mathf.Sin(maxAngle / length * i * Mathf.Deg2Rad);
                            if (steeringAngle > 0)
                            {
                                trackRight.Add(new Vector3(x, 0, z - rMin));
                            }
                            else
                            {
                                trackRight.Add(new Vector3(x, 0, -(z - rMin) + carWidth));
                            }

                            x = -rMax * Mathf.Cos(maxAngle / length * i * Mathf.Deg2Rad);
                            z = rMax * Mathf.Sin(maxAngle / length * i * Mathf.Deg2Rad);
                            if (steeringAngle > 0)
                            {
                                trackLeft.Add(new Vector3(x, 0, z - rMin));
                            }
                            else
                            {
                                trackLeft.Add(new Vector3(x, 0, -(z - rMin) + carWidth));
                            }
                        }
                    }
                    trackRight[trackRight.Count - 1] = Vector3.forward * trackRight[trackRight.Count - 1].z;
                    trackLeft[trackLeft.Count - 1] = Vector3.forward * trackLeft[trackLeft.Count - 1].z;
                }
            }
            track[0] = trackLeft.ToArray();
            track[1] = trackRight.ToArray();
            trackLeft = trackRight = null;
            return track;
}