Add curvature to the rendering without changing simulation code.

CurveController.cs

using UnityEngine;

namespace AIEngineTest
{
    public class CurveController : MonoBehaviour
    {
        private static CurveController s_Instance = null;

        private const float k_StraightDistanceClamp = 50f;
        private const float k_CurvatureClamp = 10f;

        [SerializeField] [Range(0f, k_StraightDistanceClamp)] private float m_StraightDistance = 10f;
        [SerializeField] [Range(-k_CurvatureClamp, k_CurvatureClamp)] private float m_VerticalCurvature = 0f;
        [SerializeField] [Range(-k_CurvatureClamp, k_CurvatureClamp)] private float m_HorizontalCurvature = 0f;

        private static readonly int s_StraightRenderDistanceID = Shader.PropertyToID("_CURVER_STRAIGHT_RENDER_DISTANCE");
        private static readonly int s_HorizontalCurvatureID = Shader.PropertyToID("_CURVER_HORIZONTAL_CURVATURE");
        private static readonly int s_VerticalCurvatureID = Shader.PropertyToID("_CURVER_VERTICAL_CURVATURE");

        private void Awake()
        {
            if (s_Instance == null)
            {
                s_Instance = this;
            }
            else
            {
                Debug.Log("Duplicate curve controller detected.", this);
                return;
            }

            UpdateValues();
        }

        private void OnDestroy()
        {
            if (s_Instance == this)
            {
                s_Instance = null;
            }
        }

        private void OnValidate()
        {
            UpdateValues();
        }

        private void UpdateValues()
        {
            straightDistance = m_StraightDistance;
            horizontalCurvature = m_HorizontalCurvature;
            verticalCurvature = m_VerticalCurvature;
        }

        public float straightDistance
        {
            get => m_StraightDistance;
            set
            {
                value = Mathf.Clamp(value, 0f, k_StraightDistanceClamp);
                m_StraightDistance = value;
                Shader.SetGlobalFloat(s_StraightRenderDistanceID, value);
            }
        }

        public float horizontalCurvature
        {
            get => m_HorizontalCurvature;
            set
            {
                value = Mathf.Clamp(value, -k_CurvatureClamp, k_CurvatureClamp);
                m_HorizontalCurvature = value;
                Shader.SetGlobalFloat(s_HorizontalCurvatureID, value);
            }
        }

        public float verticalCurvature
        {
            get => m_VerticalCurvature;
            set
            {
                value = Mathf.Clamp(value, -k_CurvatureClamp, k_CurvatureClamp);
                m_VerticalCurvature = value;
                Shader.SetGlobalFloat(s_VerticalCurvatureID, value);
            }
        }
    }
}

Curver.hlsl

// this file is meant to be used in conjunction with a Custom Function node
// in ShaderGraph. You can find out more about how to use it at
// https://docs.unity3d.com/Packages/[email protected]/manual/Custom-Function-Node.html

// all you need is the Position node (Object Space), connect its input to VertexPosOS and optionally
// provide an origin to determine where the rendering looks straight (and not curved)

#ifndef CURVER_INCLUDED
#define CURVER_INCLUDED

#include "Packages/com.unity.render-pipelines.core/ShaderLibrary/SpaceTransforms.hlsl"

uniform float _CURVER_STRAIGHT_RENDER_DISTANCE;
uniform float _CURVER_HORIZONTAL_CURVATURE;
uniform float _CURVER_VERTICAL_CURVATURE;

#define CURVER_CURVATURE_POWER 2

void GetModifiedObjectSpace_float(const float3 OriginWS, const float3 VertexPosOS, out float3 ModifiedVertexPosOS)
{
    const float3 VertexPosWS = TransformObjectToWorld(VertexPosOS);

    const float DistanceToCamera = distance(OriginWS, VertexPosWS);

    const float StraighteningMask = step(_CURVER_STRAIGHT_RENDER_DISTANCE, DistanceToCamera);

    const float2 Curvature = pow(DistanceToCamera - _CURVER_STRAIGHT_RENDER_DISTANCE, CURVER_CURVATURE_POWER)
        * float2(_CURVER_HORIZONTAL_CURVATURE, _CURVER_VERTICAL_CURVATURE) * pow(0.1f, CURVER_CURVATURE_POWER);

    const float3 ModifiedVertexPosWS = VertexPosWS + (StraighteningMask * float3(Curvature.x, Curvature.y, 0));

    ModifiedVertexPosOS = TransformWorldToObject(ModifiedVertexPosWS);
}

void GetModifiedObjectSpace_half(const half3 OriginWS, const half3 VertexPosOS, out half3 ModifiedVertexPosOS)
{
    const half3 VertexPosWS = TransformObjectToWorld(VertexPosOS);

    const half DistanceToCamera = distance(OriginWS, VertexPosWS);

    const half StraighteningMask = step(_CURVER_STRAIGHT_RENDER_DISTANCE, DistanceToCamera);

    const half2 Curvature = pow(DistanceToCamera - _CURVER_STRAIGHT_RENDER_DISTANCE, CURVER_CURVATURE_POWER)
        * half2(_CURVER_HORIZONTAL_CURVATURE, _CURVER_VERTICAL_CURVATURE) * pow(0.1f, CURVER_CURVATURE_POWER);

    const half3 ModifiedVertexPosWS = VertexPosWS + (StraighteningMask * half3(Curvature.x, Curvature.y, 0));

    ModifiedVertexPosOS = TransformWorldToObject(ModifiedVertexPosWS);
}

#undef CURVER_CURVATURE_POWER

#endif