[Unity] Create lines at runtime (use of Bezier)
1. Goals achieved
Create a mesh curve on the fly that can be edited in real time using Bezier methods.
2. Principle introduction
2.1 Creation of curves
To create a mesh curve in Unity, you can refer to the implementation method of Unity's procedural mesh . Mainly divided into vertices, triangles, UVs and normals. The author has a similar article: Pure code creation method of unity cord pipeline_ , which explains in detail the creation method of grid lines. The difference this time is the method of establishing normal lines.
2.2 Establishment of Bezier curve points
The author has an article Creation of Bezier Curve in Unity_describing the creation method of Bezier.
3. Implementation process
3.1 How to create curves
Principles of Line Composition
A curve is composed of a cross-section circle and a central axis. The normal direction of the cross section is the vector difference between the front and rear points. The green line in the figure below is the central axis, point A is the point of the cross section, and the normal direction of the cross section is the vector AD ⃗ \vec{AD}ADThe vector CB ⃗ \vec{CB}CBThe unit vector of ; the normal direction of the end point and starting point is the vector of itself and the previous or next point.
Code source code
3.1.1 Creation of transverse circle
#region 横切圆创建
/// <summary>
/// 得到管线横切圆
/// </summary>
/// <param name="Count">段数</param>
/// <param name="R">半径</param>
/// <returns></returns>
Vector3[] CircularSection(int Count, float R)
{
Vector3[] vector3s = new Vector3[Count];
float angle = 360 / Count;
Vector3 vector3 = new Vector3(R, 0, 0);
for (int i = 0; i < Count; i++)
{
//根据角度得到圆的分布点
vector3s[i] = vector3.ToAngle(angle * i, Vector3.zero, Vector3.forward);
}
return vector3s;
}
#endregion
vector3 rotation extension method
/// <summary>
/// 角度旋转
/// </summary>
/// <param name="vector3"></param>
/// <param name="angle">旋转角度</param>
/// <param name="center">旋转中心点</param>
/// <param name="direction">旋转轴</param>
/// <returns></returns>
public static Vector3 ToAngle(this Vector3 vector3, float angle, Vector3 center, Vector3 direction)
{
Vector3 pos = center;
Quaternion quaternion = Quaternion.AngleAxis(angle, direction);
Matrix4x4 matrix = new Matrix4x4();
matrix.SetTRS(pos, quaternion, Vector3.one);
vector3 = matrix.MultiplyPoint3x4(vector3);
return vector3;
}
3.1.2 Establishment of center line
class LinePoint
{
Vector3 location;
Vector3 direction;
public Vector3 Location { get => location; set => location = value; }
public Vector3 Direction { get => direction; set => direction = value; }
}
/// <summary>
/// 中心线的确立
/// </summary>
/// <param name="createPoint">曲线点</param>
/// <returns></returns>
List<LinePoint> SetLinePoint(Vector3[] createPoint)
{
List<LinePoint> pipePoints = new List<LinePoint>();
int length = createPoint.Length;
for (int i = 0; i < length; i++)
{
if (i == 0)
{
Vector3 tangent = (createPoint[i + 1] - createPoint[i]).normalized;//法线
AddPipePoints(createPoint[i], tangent, ref pipePoints);
}
else if (i == length - 1)
{
Vector3 tangent = (createPoint[i] - createPoint[i - 1]).normalized;//法线
AddPipePoints(createPoint[i], tangent, ref pipePoints);
}
else
{
Vector3 tangent = (createPoint[i+1] - createPoint[i - 1]).normalized;//法线
AddPipePoints(createPoint[i], tangent, ref pipePoints);
}
}
return pipePoints;
}
/// <summary>
/// 增加中心轴线点
/// </summary>
/// <param name="location">位置</param>
/// <param name="direction">法线</param>
void AddPipePoints(Vector3 location, Vector3 direction, ref List<LinePoint> pipePoints)
{
LinePoint pipePoint = new LinePoint();
pipePoint.Location = location;
pipePoint.Direction = direction;
pipePoints.Add(pipePoint);
}
3.1.3 Grid creation
/// <summary>
/// 立体网格创建
/// </summary>
/// <param name="createPoint">创建的点数据</param>
/// <param name="circularCount">圆的段数</param>
/// <param name="circularR">圆的半径</param>
/// <returns></returns>
public Mesh CreateLine3D(Vector3[] createPoint, int circularCount, float circularR)
{
//截面圆
Vector3[] circul = CircularSection(circularCount, circularR);
//中心线
List<LinePoint> centreLine = SetLinePoint(createPoint);
//网格点数据
Vector3[] meshPoint = CreateMeshPoint(centreLine, circul);
float uvX = Vector3.Distance(circul[0], circul[1]);
//返回网格
return CreatMesh(centreLine, meshPoint, circul.Length, uvX);
}
/// <summary>
/// 创建网格点数据
/// </summary>
/// <param name="linePoint"></param>
/// <param name="circular"></param>
/// <returns></returns>
Vector3[] CreateMeshPoint(List<LinePoint> linePoint, Vector3[] circular)
{
int length = linePoint.Count;
int circularCount = circular.Length;
Vector3[] meshPoint = new Vector3[length * circularCount];
for (int i = 0; i < length; i++)
{
for (int j = 0; j < circularCount; j++)
{
meshPoint[(i * circularCount) + j] = circular[j].FromToMoveRotation(linePoint[i].Location, linePoint[i].Direction);
}
}
return meshPoint;
}
/// <summary>
/// 网格创建
/// </summary>
/// <param name="linePoints">线的轴心线组</param>
/// <param name="meshPoint">网格点</param>
/// <param name="count">段数</param>
/// <param name="uvX">uv宽度</param>
/// <returns></returns>
Mesh CreatMesh(List<LinePoint> linePoints, Vector3[] meshPoint, int count, float uvX)
{
Mesh mesh = new Mesh();
mesh.vertices = meshPoint;
mesh.triangles = GetTriangles(linePoints.Count, count);
mesh.uv = GetUV(linePoints, count, uvX);
mesh.RecalculateNormals();
mesh.RecalculateBounds();
return mesh;
}
/// <param name="length">线段段数</param>
/// <param name="count">横截面段数（也就是圆的段数）</param>
/// <returns></returns>
int[] GetTriangles(int length, int count)
{
int[] triangles = new int[(count * (length - 1)) * 6];
int k = 0;
if (count == 1)
{
for (int i = 0; i < length-1; i++)
{
int a = i * 2;
triangles[k] = a;
triangles[k + 1] = a + 1;
triangles[k + 2] = a + 3;
triangles[k + 3] = a;
triangles[k + 4] = a + 3;
triangles[k + 5] = a + 2;
k += 6;
}
}
else
{
for (int i = 0; i < length - 1; i++)
{
for (int j = 0; j < count; j++)
{
if (j == count - 1)
{
// Debug.Log("k=" + k);
triangles[k] = (i * count) + j;
triangles[k + 1] = (i * count) + 0;
triangles[k + 2] = ((i + 1) * count) + 0;
triangles[k + 3] = (i * count) + j;
triangles[k + 4] = ((i + 1) * count) + 0;
triangles[k + 5] = ((i + 1) * count) + j;
}
else
{
triangles[k] = (i * count) + j;
triangles[k + 1] = (i * count) + j + 1;
triangles[k + 2] = ((i + 1) * count) + j + 1;
triangles[k + 3] = (i * count) + j;
triangles[k + 4] = ((i + 1) * count) + j + 1;
triangles[k + 5] = ((i + 1) * count) + j;
}
k += 6;
}
}
}
return triangles;
}
/// <summary>
/// 创建uv
/// </summary>
/// <param name="linePoints"></param>
/// <param name="count"></param>
/// <param name="uvX"></param>
/// <returns></returns>
Vector2[] GetUV(List<LinePoint> linePoints,int count, float uvX)
{
int length = linePoints.Count;
if (count == 1) { count = 2; }
Vector2[] uvs = new Vector2[(count * length)];
float lineDis = 0;
int k = 0;
for (int i = 0; i < length; i ++)
{
if (i != 0)
{
lineDis += Vector3.Distance(linePoints[i].Location, linePoints[i - 1].Location);
}
for (int j = 0; j < count; j++)
{
Vector2 vector2;
if (j % 2 != 0)
{
vector2 = new Vector2(uvX, lineDis);
}
else
{
vector2 = new Vector2(0, lineDis);
}
uvs[k] = vector2;
k += 1;
}
}
return uvs;
}
3.2 Method of establishing Bezier curve
Source code
/// <summary>
/// 获取绘制点
/// </summary>
/// <param name="controlPoints"></param>
/// <param name="segmentsPerCurve"></param>
/// <returns></returns>
public List<Vector3> GetDrawingPoints(List<Vector3> controlPoints, int segmentsPerCurve)
{
List<Vector3> points = new List<Vector3>();
// 下一段的起始点和上段终点是一个，所以是 i+=3
for (int i = 0; i <= controlPoints.Count - 4; i += 3)
{
var p0 = controlPoints[i];
var p1 = controlPoints[i + 1];
var p2 = controlPoints[i + 2];
var p3 = controlPoints[i + 3];
float dis = Vector3.Distance(p0, p3);
int count = Mathf.CeilToInt(segmentsPerCurve * dis);
if (count < segmentsPerCurve)
{
count = segmentsPerCurve;
}
for (int j = 0; j <= count; j++)
{
var t = j / (float)count;
points.Add(CalculateBezierPoint(t, p0, p1, p2, p3));
}
}
return points;
}
// 三阶公式
Vector3 CalculateBezierPoint(float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
{
Vector3 result;
Vector3 p0p1 = (1 - t) * p0 + t * p1;
Vector3 p1p2 = (1 - t) * p1 + t * p2;
Vector3 p2p3 = (1 - t) * p2 + t * p3;
Vector3 p0p1p2 = (1 - t) * p0p1 + t * p1p2;
Vector3 p1p2p3 = (1 - t) * p1p2 + t * p2p3;
result = (1 - t) * p0p1p2 + t * p1p2p3;
return result;
}
3.3 Bezier curve application
Based on the above method, the Bezier creation, saving, reading, and editing functions are implemented.
Case download address
Create curve
save curve
There are two storage methods: long-term storage and temporary storage. Long-term saving is to write the saved data to a local file, which can be read even after the project is restarted; temporary saving is to save the data while the project is running and will be lost after restarting. The demo uses the temporary saving method
Read and edit
After reading the curve, you can continue to edit the current curve.
Curve browsing
