What is a regular curve?

A differentiable curve is said to be regular if its derivative never vanishes. ( In words, a regular curve never slows to a stop or backtracks on itself.) Two differentiable curves and. are said to be equivalent if there is a bijective map. such that the inverse map.

Regarding this, how do you define a curve?

Curve - Definition with Examples. What is Curve? A curve is a continuous and smooth flowing line without any sharp turns. One way to recognize a curve is that it bends and changes its direction at least once.

Beside above, what is smooth curve? A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous map from a one-dimensional space to an. -dimensional space which on its domain has continuous derivatives up to a desired order.

People also ask, can a curve be straight?

A curve is not a straight line, just as a straight line is not a curve. A curved line contains points that are not linear to two given points. The curve moves in other directions from the straight line created by joining collinear points.

What is unit speed curve?

Unit speed curve parameterization. If you change the time parameterization by inverting this function, solving for t as a function of s, then the total length of curve traversed by p(t(s)) up to time s is s. This is called either the unit speed parameterization or parameterization by arc length.

29 Related Question Answers Found

What is a space curve?

Space Curve. A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane.

What is the torsion of a plane curve?

Answered Feb 9, 2017. In the elementary differential geometry of curves in three dimension, the torsion of a curve measures how sharply it is twisting out of the plane of curvature. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve.

WHAT IS curve in geometry?

In analytic geometry, a curve is continuous map from a one-dimensional space to an -dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve. The simplest curves can be represented parametrically in -dimensional space as.

What is curvature in differential geometry?

In differential geometry , curvature is the rate of change of direction of a curve at a point on that curve , or the rate of change of inclination of the tangent to a certain curve relative to the length of arc .

What is torsion in differential geometry?

In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The difference between a connection with torsion, and a corresponding connection without torsion is a tensor, called the contorsion tensor.

What are different types of curves?

Let us now try to understand the different types of curves which have varying definitions and properties.

Simple Curve. As we know, a curve is a line that is not straight.
Closed Curve.
Simple Closed Curve.
Algebraic and Transcendental Curve.
Algebraic Curve.
Transcendental Curve.

How do you graph a curve?

Draw a curve

On the Insert tab, click Shapes.
Under Lines, click Curve.
Click where you want the curve to start, drag to draw, and then click wherever you want to add a curve.
To end a shape, do one of the following: To leave the shape open, double-click at any time. To close the shape, click near its starting point.

What is simple curve with example?

In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves. The shape which is not closed by line-segments or a curve is called an open curve. A closed curve which does not cross itself is called a simple closed curve.

What are curves in a woman?

BODY CURVES:

If her body parts diverge from the straight line around her calves, thighs, butt, hips, waist, and breasts, she is known to have a curvy body. Basically all the body parts create a curve shape and that is the real beauty of any of the girls.

What is a curved structure called?

An arch is a structure that is curved at the top and is supported on either side by a pillar, post, or wall. If something arches in a particular direction, it makes a curved line or movement.

Is circle a curved line?

Yes, a circle (that is, the circumference, not the interior) is a curve. In fact, it's a closed curve. Also, parabolas, hyperbolas, and ellipses are curves. Even straight lines are curves, although the curvature of a straight line is zero.

What is vertical line?

A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane. In the figure above, drag either point and note that the line is vertical when they both have the same x-coordinate. A vertical line has no slope. Or put another way, for a vertical line the slope is undefined.

What does a curve in a graph mean?

A curved line on a graph means “change”! A curved line on a graph means “change”!

What is the top of a curve called?

The absolute top of the arch is the apex. The curve at the top of the arch is known as the crown. The point at which the curve begins is the springing or spring-line.

What do you mean by curve?

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line which does not have to be straight. This definition of a curve has been formalized in modern mathematics as: A curve is the image of a continuous function from an interval to a topological space.

How do you smooth a curve?

Smooth a curve

Select the curve, or select only the CVs you want to smooth.
Select Curves > Smooth. To control the amount of smoothing, choose Curves > Smooth > and set the Smoothness option. Lower values do less smoothing. The default value is 10.

What is C infinity function?

C^infty Function. A function is a function that is differentiable for all degrees of differentiation. For instance, (left figure above) is because its th derivative exists and is continuous. All polynomials are . The reason for the notation is that C-k have.