Normal Vector to the Surface
The normal vector to a surface at a given point is a vector that is perpendicular to the tangent plane at that point. It represents the direction in which the surface is “pointing” or facing locally.
- To find the normal vector to a surface, you typically compute the gradient of the surface equation at the given point.
- The gradient is a vector composed of the partial derivatives of the surface equation with respect to each variable (usually x, y, and z).
- At the point of interest, the gradient vector points in the direction of the steepest ascent of the surface.
- By normalizing this gradient vector, you obtain the normal vector to the surface at that point.
- This normal vector is used in various applications, such as computing surface normal in computer graphics or determining the direction of maximum curvature on a surface.
Tangent Plane to a Surface
A tangent plane is a flat surface that touches a curve or surface at a single point, sharing the same slope or direction at that point, facilitating local approximation in calculus. This article discusses tangent planes, which are flat surfaces that touch curves or surfaces at specific points. It explains their definition, how to calculate them, and their geometric interpretation. It also explores their applications in various fields like engineering, physics, and computer graphics.
Table of Content
- Definition of Tangent Plane
- How to Find the Tangent Plane to a Surface
- Tangent Plane Equation
- Geometric Interpretation of the Tangent Plane
- Applications of Tangent Plane to a Surface