How can a cubic Bezier curve be constructed to have a tangent to a circle?

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In summary, a Bezier curve is a mathematical curve commonly used in computer graphics and animation, defined by a set of control points. Tangency of the curve refers to the point where it meets a straight line, and is important in determining its smoothness and continuity. Tangency is calculated by finding the point where the slope of the curve is equal to the slope of the tangent line, and is crucial in creating realistic and visually appealing graphics. It is also used in various applications such as computer graphics, animation, design software, engineering, and architecture.
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mymachine
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Can anyone describe a tangency of Bezier curve such as below image?
 

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This is a pretty vague request. Can you be more specific?
 
  • #3
SteamKing said:
This is a pretty vague request. Can you be more specific?

The circle is construct first.

Then how construct a Bezier curve, say, a cubic Bezier curve, which has its tangent to the circle?

I hope you understand.
 

What is a Bezier curve?

A Bezier curve is a mathematical curve that is commonly used in computer graphics and animation. It is defined by a set of control points that determine its shape and direction.

What is tangency of the Bezier curve?

Tangency of the Bezier curve refers to the point where the curve meets a straight line, also known as the tangent line. This point is important in determining the smoothness and continuity of the curve.

How is tangency calculated in a Bezier curve?

Tangency in a Bezier curve is calculated by finding the point where the slope of the curve is equal to the slope of the tangent line. This can be done using mathematical equations or through geometric constructions.

Why is tangency important in Bezier curves?

Tangency is important in Bezier curves because it helps to ensure smooth and continuous curves, which are essential in creating realistic and visually appealing graphics. It also allows for precise control over the shape and direction of the curve.

What are some applications of tangency in Bezier curves?

The concept of tangency in Bezier curves is used in many applications, including computer graphics, animation, and design software. It is also used in engineering and architecture for creating smooth and precise curves in 3D models and CAD drawings.

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