Bezier and Ferguson Curves
FERGUSON AND BEZIER CURVES Palash Luthra Sachin Maheshwari Netaji Subhas Institute of Technology New Delhi-110078 India 1. CURVES-DEFINITION 2. NEED OF CURVES March 2013
A line or outline that gradually deviates from being straight for some or all of its length.
Curves play a very significant role in CAD modeling, especially, for generating a wireframe model, which is the simplest form for representing a model. We can display an object on a monitor screen in three different computer-model forms: • Wireframe model – It consist of points and curves only. Advantages of this type of model include ease of creation and low level hardware and software requirements. Additionally, the data storage requirement is low. The main disadvantage of a wireframe model is that it can be very confusing to visualize. • Surface Model- sweeping a curve around or along an axis can create a surface model. Surface models are useful for representing surfaces such as a soft-drink bottle, automobile fender, aircraft wing, and in general, any complicated curved surface. • Solid model -Solid models represent objects in a very realistic and unambiguous form; however, they require a large amount of storage memory and high-end computer hardware. A solid model can be shaded and rendered in desired colors to give it a more realistic appearance. 3. ROLE OF CURVES IN GEOMETRIC MODELING
Curves are used to draw a wireframe model, which consists of points and curves; the curves are utilized to generate surfaces by performing parametric transformations on them. A curve can be as simple as a line or as complex as a B-spline. In general, curves can be classified as follows: • Analytical Curves: This type of curve can be represented by a simple mathematical equation, such as, a circle or an ellipse. They have a fixed form and cannot be modified to achieve a shape that violates the mathematical equations. • Interpolated curves: An interpolated curve is drawn by interpolating the given data points and
A line or outline that gradually deviates from being straight for some or all of its length.
Curves play a very significant role in CAD modeling, especially, for generating a wireframe model, which is the simplest form for representing a model. We can display an object on a monitor screen in three different computer-model forms: • Wireframe model – It consist of points and curves only. Advantages of this type of model include ease of creation and low level hardware and software requirements. Additionally, the data storage requirement is low. The main disadvantage of a wireframe model is that it can be very confusing to visualize. • Surface Model- sweeping a curve around or along an axis can create a surface model. Surface models are useful for representing surfaces such as a soft-drink bottle, automobile fender, aircraft wing, and in general, any complicated curved surface. • Solid model -Solid models represent objects in a very realistic and unambiguous form; however, they require a large amount of storage memory and high-end computer hardware. A solid model can be shaded and rendered in desired colors to give it a more realistic appearance. 3. ROLE OF CURVES IN GEOMETRIC MODELING
Curves are used to draw a wireframe model, which consists of points and curves; the curves are utilized to generate surfaces by performing parametric transformations on them. A curve can be as simple as a line or as complex as a B-spline. In general, curves can be classified as follows: • Analytical Curves: This type of curve can be represented by a simple mathematical equation, such as, a circle or an ellipse. They have a fixed form and cannot be modified to achieve a shape that violates the mathematical equations. • Interpolated curves: An interpolated curve is drawn by interpolating the given data points and
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