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Monotone data visualization using rational trigonometric spline interpolation.

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Summary
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New rational trigonometric schemes conserve monotonicity for curve and surface data. These methods use constrained parameters in rational cubic and bicubic functions for shape control and data fidelity.

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Area of Science:

  • Computer-Aided Design (CAD)
  • Geometric Modeling
  • Numerical Analysis

Background:

  • Maintaining data monotonicity is crucial in curve and surface representation.
  • Existing methods may struggle to preserve monotonicity while allowing shape flexibility.

Purpose of the Study:

  • To develop novel rational cubic and bicubic trigonometric schemes.
  • To ensure the conservation of monotonicity for curve and surface data.
  • To provide shape control through parameter adjustments.

Main Methods:

  • Development of rational cubic trigonometric functions with four parameters per subinterval.
  • Development of rational bicubic partially blended trigonometric functions with eight parameters per patch.
  • Imposition of constraints on specific parameters to guarantee monotonicity preservation.

Main Results:

  • Successfully retained monotonicity of curve and surface data using the developed schemes.
  • Demonstrated the ability to modify curve and surface shapes by adjusting free parameters.
  • Mathematical verification and graphical demonstrations confirmed the algorithm's efficacy.

Conclusions:

  • The proposed rational trigonometric schemes effectively preserve data monotonicity.
  • These methods offer a balance between data fidelity and shape manipulation capabilities.
  • The algorithms are mathematically sound and graphically validated for practical applications.