将 Z 轴与矢量对齐的最简单方法是什么? [英] What is the easiest way to align the Z axis with a vector?

问题描述

给定一个点(例如 (0, 0, 0))和一个向量(例如 (x, y, z)).对齐以 (0, 0, 0) 为中心的负 Z 轴指向该向量方向的最简单方法是什么?欢迎提供使用 OpenGL 的示例，但不是必需的.

Given a point such as (0, 0, 0) and a vector like (x, y, z). What is the easiest way to align the negative Z-axis centered at (0, 0, 0) to point in the direction of this vector? Examples using OpenGL would be welcome, but not neccessary.

推荐答案

有很多不同的方法可以旋转坐标系以指向给定方向；它们都会让 z 轴指向您想要的方向，但 x 轴和 y 轴的方向会有所不同.

There's lots of different ways to rotate a coordinate-frame to point in a given direction; they'll all leave the z-axis pointed in the direction you want, but with variations in how the x- and y-axes are oriented.

以下内容可为您提供最短的旋转时间，这可能是您想要的，也可能不是.

The following gets you the shortest rotation, which may or may not be what you want.

vec3 target_dir = normalise( vector );
float rot_angle = acos( dot_product(target_dir,z_axis) );
if( fabs(rot_angle) > a_very_small_number )
{
    vec3 rot_axis = normalise( cross_product(target_dir,z_axis) );
    glRotatef( rot_angle, rot_axis.x, rot_axis.y, rot_axis.z );
}

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