# Normal's

Table of Contents

## Normal’s

Within the CAD system, the base geometric elements, Surface’s (Super Class), Curve’s (Super Class) have an inheritable attribute, known as the Surface or Curve normal dependent on the element in discussion. This attribute is essentially a direction or direction(s) which describes for a curve the start to end direction and for a surface, the material side and at any given point an offset direction which is always perpendicular to the surface.

### Curves – Super Class

The super class Curve is defined by sub-classes consisting of; Lines, Polylines, Arc’s, Circles, Splines, Bezier Curves, Non-Uniform Rational Bezier Splines (NURBS), and Non-Uniform Rational Polynomial Splines NURPS. They all have one thing in common a start and and end point (Circles do have a natural break point at 3 O’clock), which means you can construct a direction from the start to the end point, to help define the Normal direction of the element. The hard thing is to not think of this necessarily as a vector direction but as a direction construct which could be a vector, or rotation in some cases.

#### Lines

Let’s start of with a simple Line drawn from Point(A) to Point(B), if this was a vector we would know that the direction of the vector from was Point(A) to Point(B), fortunately this rule also applies for the direction of a line. If we were to draw the line from Point(B) to Point(A) then the direction would run from Point(B) to Point(A). Line

#### Planes

Quick note: – a Plane is really a mathematically perfectly flat surface, and at any given point across the plane the Normal’s will all be parallel and in the same direction. Based on how the plane is constructed will define the directions orientation, and there are two ways in which direction is defined either inheritance, or the culmination of parental vectors in conjunction with the left-hand rule.

We will get into this in more detail later. Plane

### Inheritance

Inheritance is defined by the genetic characters transmitted from parent to offspring, the same is also true within the CAD environment. Let’s go back to our line example, if the Line is constructed from Point(A) to Point(B), then the lines direction is from Point(A) to Point(B). In addition if a plane is constructed perpendicular to the line through point on the line then the plane will inherit the normal direction of the line. Plane from Line Inheritance

Subsequently, if a plane is offset from the first plane then the second plane will inherit the normal direction from the first plane. Offset Plane Inheritance

### Left-Hand Rule (Right-Hand Rule)

This is somewhat subjective in 3D space based on your context and point of view, where it’s Left or Right-Hand rule, but the underlying principle still applies. For this well look at a plane defined by two lines, we know that the lines have directions based on how they were drawn in this case both lines are drawn from Point(A) to Points(B, and C). The plane is created through the two lines, and in-keeping with a mathematical approach we can assume that the Vector Cross Product is used to define the Vector of the Plane. However well use the Left-Hand rule as a general rule, when defining directions for features, when there is more than one direction base feature used to define a new feature. Left-Hand Rule

Just as a final clarification, in the case where on offset plane is create, the offset plane only has one parent, so we know that inheritance applies. In all other cases the Left-Hand rule will apply.