Question

我想绘制我的对象将遵循的平滑*和随机路径，我决定使用二次贝塞尔曲线（但我对其他想法持开放态度）。

我的代码以随机但不流畅的方式移动我的对象。

我的问题是：如何让方向变得更顺畅？我应该完全放弃我的Bezier解决方案，还是有办法让我的代码能够达到我想要的目标？

* smooth ==没有突然改变方向

我的代码：

using UnityEngine;
using System.Collections;
using System.Collections.Generic;

public class Lights : MonoBehaviour {
    public float paintHeight = -90.0f;
    public static int NUMBER_OF_LIGHTS = 3;
    private static int BEZIER_PATH_POINTS = 100;
    private float GOLDEN_COLOR_RATIO = 0.618033988749895f;
    private Light[] lights = new Light[NUMBER_OF_LIGHTS];

    Vector3 RandomPoint() {
        float obj_width = gameObject.GetComponent<RectTransform>().rect.width;
        float screenX = Random.Range(-obj_width / 2, obj_width / 2);

        float obj_height = gameObject.GetComponent<RectTransform>().rect.height;
        float screenY = Random.Range(-obj_height / 2, obj_height / 2);

        return new Vector3(screenX, screenY, -paintHeight);
    }


    Vector3 QuadraticBezierPoint(Vector3 startPoint, Vector3 endPoint, Vector3 vertexPoint, float t) {
        /*
         *         vertex
         *        /╲
         *       /   ╲
         *      /  p   ╲
         *     /  . .    ╲
         *    / .      ·   ╲
         *   /·           ·  ╲
         *  start           · end
         *
         *  0 < t < 1
         *
         * B(t) = (1 - t)^2 * P0 + 2 * (1-t) * t * P1 + t^2 * P2
         * 
         */
        return Mathf.Pow((1 - t), 2) * startPoint + 2 * (1 - t) * t * vertexPoint + Mathf.Pow(t, 2) * endPoint;
    }

    Color RandomColor() {
        float h = Random.Range(0.0f, 1.0f) + GOLDEN_COLOR_RATIO;
        h %= 1;
        return Color.HSVToRGB(h, 0.99f, 0.99f);
    }

    void Start() {
        for (int i = 0; i < NUMBER_OF_LIGHTS; i++) {
            GameObject light_obj = new GameObject();
            Light light = light_obj.AddComponent<Light>();
            light.type = LightType.Point;
            light.range = 10.0f;
            light.intensity = 3.5f;
            light.renderMode = LightRenderMode.ForcePixel;
            light.name = "Light" + i;
            light.transform.parent = gameObject.transform;
            lights[i] = light;
        }

        StartCoroutine("Move");
    }

    IEnumerator Move () {
        Dictionary<string, Vector3>[] light_points = new Dictionary<string, Vector3>[NUMBER_OF_LIGHTS];
        Dictionary<string, Color>[] light_colors = new Dictionary<string, Color>[NUMBER_OF_LIGHTS];
        for (int i = 0; i < NUMBER_OF_LIGHTS; i++) {
            light_points[i] = new Dictionary<string, Vector3>();
            light_colors[i] = new Dictionary<string, Color>();
            //light_points[i]["startPoint"] = RandomPoint();
            //light_points[i]["vertexPoint"] = RandomPoint();
            light_points[i]["endPoint"] = RandomPoint();
            light_colors[i]["nextColor"] = RandomColor();
        }

        while(true) {
            for (int i = 0; i < NUMBER_OF_LIGHTS; i++) {
                light_points[i]["startPoint"] = light_points[i]["endPoint"];
                light_points[i]["vertexPoint"] = RandomPoint();
                light_points[i]["endPoint"] = RandomPoint();

                light_colors[i]["currentColor"] = light_colors[i]["nextColor"];
                light_colors[i]["nextColor"] = RandomColor();
            }

            for (int i = 0; i < BEZIER_PATH_POINTS; i++) {
                float percent = (float)i / BEZIER_PATH_POINTS;
                for (int j = 0; j < NUMBER_OF_LIGHTS; j++) {
                    lights[j].transform.localPosition = QuadraticBezierPoint(
                        light_points[j]["startPoint"],
                        light_points[j]["endPoint"],
                        light_points[j]["vertexPoint"],
                        percent
                    );
                    lights[j].color = Color.Lerp(light_colors[j]["currentColor"], light_colors[j]["nextColor"], percent);
                }
                yield return new WaitForSeconds(0.02f);
            }
        }
    }
}

Answer 1

如果你的曲线从A到B有一些中点，你必须相应地选择一个C，这样B的角度（A，B，C）就不会太小或太大。

此外，您必须以适当的方式选择中间点，例如， https://www.particleincell.com/2012/bezier-splines/，因此方向的变化不会太大。

Answer 2

您可以一直使用NURBS或其他样条线，但是根据您发布的内容，可能有一种更简单，更简洁的方法来获得平滑曲线。

您创建的每条曲线在代码的开头，顶点和结尾都有3个点。让我们称它们为S，V和E.另外，让我们看一下它们，所以{S0,V0,E0}制作第一条曲线，{S1,V1,E1}制作第二条曲线，等等。

现在您确保S1=E0，S2=E1等等。这意味着您的灯光不会随机跳跃，但切换Bezier曲线时动作可能会突然发生。

为确保动作顺畅，请尝试确保S1 = E0 = 0.5 * (V0+V1)。在实践中，这意味着你随机生成S0和V0。然后，对于每条新曲线，您将生成一个新的V，旧V和新V之间的中点是曲线断点。

这相当于具有均匀度2 B样条。

以下是一些可能具有说明性的示例代码。

// initialize with randomness
// we need a previous v and a current v for the first iteration
// So, the first start point will be halfway between these two points
prev_v = random_point()
v = random_point()

while( true )
{
    next_v = random_point()
    s = 0.5 * (prev_v + v) // s is halfway between prev_v and v
    e = 0.5 * (v + next_v) // e is halfway between v and next_v
    yield_movement_bezier( s, v, e )

    // prep for next iteration
    prev_v = v
    v = next_v
}

使用二次贝塞尔曲线绘制随机路径

2 个答案: