Normal is widely used in mathematics, physics, engineering and other fields. The significance and function of normals in different fields are different. I introduce normals from four aspects: mathematics, optics, computer graphics and mechanical engineering.

First, the normality in mathematics.

In plane geometry, normal refers to a straight line perpendicular to the tangent of a point on the plane. It is the vertical line projected by a tangent point on the plane, which can be obtained by finding the negative reciprocal of the tangent slope. In curve fitting, the normal is used to describe the tangent of a point on the curve to the vertical line of the plane where the point is located.

Second, the normal in optics.

In optics, normal is an important concept to describe the reflection and refraction of light on the interface. When light propagates from one medium to another, it will be reflected and refracted at the interface. The normal is a straight line perpendicular to a point on the interface, which can be divided into two parts: the incident surface and the reflecting surface. When light propagates on the incident side, the angle between its direction and the normal is called the incident angle.

When propagating on the reflection side, the angle between its direction and the normal is called the reflection angle. For the phenomenon of total reflection, light will be totally reflected at the interface, and the normal is the critical line of total reflection at the interface.

Thirdly, the normal in computer graphics.

In computer graphics, normals are vectors that describe the surface direction of three-dimensional objects. The normal vector of each surface defines a plane tangent to the surface and perpendicular to every point on the surface.

Normal vector plays an important role in calculating the reflection and refraction of light and texture mapping. In computer graphics, the normal vector of a surface can be obtained by calculating the geometric center and triangular mesh of the surface.

Four, normal in mechanical engineering

In mechanical engineering, normal is a straight line tangent to the surface of mechanical parts and perpendicular to the surface. It is usually used to describe the contour shape and curvature of the surface of a part. By calculating the normal slope, the curvature center and direction of the part surface can be determined.

In mechanical manufacturing, normals are often used in parts modeling, machining and testing, such as curve and surface fitting, numerical control programming, measurement error analysis and machine vision.

In a word, normals have different applications in different fields. Normal is an important concept in mathematics, optics, computer graphics and mechanical engineering.

It is helpful to describe the geometric shape of objects, the law of light propagation and the surface contour of parts. By deeply understanding the concept and function of normal, we can better master the knowledge and application skills in related fields.