沿着三维曲线渲染圆形

Question

沿着三维曲线渲染圆形

c++openglcomputational-geometrycurveglm-math

4

我正在尝试在3D曲线的每个点周围渲染圆圈。基本上是为曲线创建管状结构。但是，如图所示，圆的方向是错误的。下面是在计算弗雷内框架后圆对象的模型矩阵计算。我错在哪里了？参考资料，绿线是切线，蓝线是法线，红线是副法线。

Frenet Frame Calculations：

glm::vec3 pointback = curve_points[i-1];
glm::vec3 pointmid = curve_points[i];
glm::vec3 pointforward = curve_points[i+1];

glm::vec3 forward_tangent_vector =  glm::vec3(glm::normalize(pointforward - pointmid)) ;
glm::vec3 backward_tangent_vector = glm::vec3(glm::normalize(pointmid - pointback)) ;

glm::vec3 second_order_tangent = glm::normalize(forward_tangent_vector - backward_tangent_vector);

glm::vec3 binormal = glm::normalize(glm::cross(forward_tangent_vector, second_order_tangent));

glm::vec3 normal = glm::normalize(glm::cross(binormal, forward_tangent_vector));

用于圆形计算的模型矩阵

glm::mat3 tbn = glm::mat3(forward_tangent_vector,binormal,normal);

glm::vec3 normal_axis = glm::vec3(0, 1, 0);
//normal_axis = forward_tangent_vector;

glm::vec3 circleNormal = glm::normalize(tbn * normal_axis);
glm::vec3 rotationAxis = glm::cross(normal_axis, circleNormal);
float rotationAngle = glm::acos(glm::dot(normal_axis, circleNormal));

R = glm::rotate(R, glm::degrees(rotationAngle), rotationAxis);

T = glm::translate(T, pointmid);

glm::mat4 Model = T*R;

- jaykumarark

2

圆必须由法向量和副法向量构建。 - user1196549

目前看起来它们是由切向量和法向量构建的。 - user1196549

目前它们是在循环中使用以下代码构建的： float x = 0.1f*cos(dt * i); float y = 0.f; float z = 0.1f*sin(dt * i); - jaykumarark

1

然后交换两个坐标。 - user1196549

搞定了！非常感谢！ - jaykumarark

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1个回答

网页内容由stack overflow 提供, 点击上面的

可以查看英文原文，
原文链接

- Paul Houx · Accepted Answer

最简单的方法是使用弗雷内-塞雷特坐标系，通常称为TBN坐标系或TBN矩阵。方法如下：

Sample two points on the curve. Let's call them "current" and "next".

Construct the Frenet frame as follows:

vec3 T = normalize( next - current );
vec3 B = normalize( cross( T, next + current ) );
vec3 N = normalize( cross( B, T ) );

Calculate your 2D circle, similar to this:

float x = cos( angle );
float y = sin( angle );

Now, use the Frenet frame to calculate the proper orientation:

vec3 tangent = T;
vec3 normal = normalize( B * x + N * y );
vec3 vertex = current + B * x + N * y; // note: not normalized!

您可以在这里找到易于理解的解释：http://www.blackpawn.com/texts/pqtorus/