【OpenGL】自己实现B-Spline曲线

【OpenGL】自己实现B-Spline曲线

• ​​1.绘制目标​​
• ​​2.核心代码​​
• ​​3.运行结果​​

1.绘制目标

自己实现B-Spline曲线。

2.核心代码

/TO DO///
///基于CdM公式计算B-Spline混合函数///

float bspline(float* knots, int i, int order, float u) {
  // 特殊情形：一阶B-splines
  if (order == 1) {
    if (i == 0)
    {
      if (u >= knots[i] && u <= knots[i + 1])
      {
        return 1.0;
      }
      else
      {
        return 0.0;
      }
    }
    else if (i >= 1)
    {
      if (u > knots[i] && u <= knots[i + 1])
      {
        return 1.0;
      }
      else
      {
        return 0.0;
      }
    }
  }
  // 一般情形
  else {
    // 用于存储CdM公式右边和式的第一项和第二项的值
    float b1(0.f), b2(0.f);

    // 计算CdM公式右边和式的第一项
    if (knots[i + order - 1] - knots[i] == 0)
    {
      if (u - knots[i] == 0)
      {
        b1 = bspline(knots, i, order - 1, u);
      }
      else
      {
        b1 = 0;
      }
    }
    else
    {
      float x = u - knots[i];
      float y = knots[i + order - 1] - knots[i];
      b1 = x / y * bspline(knots, i, order - 1, u);
    }

    // 计算CdM公式右边和式的第二项
    if (knots[i + order] - knots[i + 1] == 0)
    {
      if (knots[i + order] - u == 0)
      {
        b2 = bspline(knots, i + 1, order - 1, u);
      }
      else
      {
        b2 = 0;
      }
    }
    else
    {
      float x = knots[i + order] - u;
      float y = knots[i + order] - knots[i + 1];
      b2 = x / y * bspline(knots, i + 1, order - 1, u);
    }

    return b1 + b2;
  }
}

/TO DO///
绘制B-Spline曲线//

void drawBSplineCurve(float* knots, float* controlPoints, int numControlPoints, int order, int numSamples) 
{
  float a = knots[order - 1];
  float num = (knots[numControlPoints] - knots[order - 1]) / numSamples;
  glColor3f(0.0f, 0.0f, 1.0f);
  glBegin(GL_LINE_STRIP);
  for (float j = a; j <= knots[numControlPoints]; j += num)
  {
    float x = 0, y = 0, z = 0;
    for (int i = 0; i < numControlPoints; i++)
    {
      x = x + controlPoints[i * POINT_DIMS] * bspline(knots, i, order, j);
      y = y + controlPoints[i * POINT_DIMS + 1] * bspline(knots, i, order, j);
      z = z + controlPoints[i * POINT_DIMS + 2] * bspline(knots, i, order, j);
    }
    glVertex3f(x, y, z);
  }
  glEnd();
}

///

/// TO DO ///
///创建OpenGL GLU NURBS 对象并设置采样方法和采样阈值/

    NURBS_OBJ = gluNewNurbsRenderer();
    gluNurbsProperty(NURBS_OBJ, GLU_SAMPLING_METHOD, GLU_PATH_LENGTH);
    gluNurbsProperty(NURBS_OBJ, GLU_SAMPLING_TOLERANCE, 10.0);

/

/// 使用自己实现的函数绘制B-Spline曲线//

    drawBSplineCurve(KNOT_ARRAY, CONTROL_POINTS_ARRAY, NUM_POINTS, BSPLINE_ORDER, 200);

3.运行结果