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Proposal Bot/Spring/2020
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Bezier Curves
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Author: Tyler Galgas
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[av_heading tag=’h1′ padding=’10’ heading=’Introduction ‘ color=” style=” custom_font=” size=” subheading_active=” subheading_size=’15’ custom_class=” admin_preview_bg=” av-desktop-hide=” av-medium-hide=” av-small-hide=” av-mini-hide=” av-medium-font-size-title=” av-small-font-size-title=” av-mini-font-size-title=” av-medium-font-size=” av-small-font-size=” av-mini-font-size=”][/av_heading]
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Bezier curve is the name given to the parametric curve controlled by a set of points. Used often in computer graphics, animations and fonts, Quadratic Bezier curves are composited together to form a sequence of curves.
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Stuff we will put here woohoo…
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As defined by Pierre Bezier
- The Bezier curve is always constrained to a polygon called a convex hull determined by it’s control points.
- The shape of the curve generally follows the shape of the polygon; the first and last points of the curve fall on the first and last points of the polygon.
- The degree of the polynomial is the number of control points minus one.
- The order of the polynomial is equal to the number of control points.
- Bezier curves exhibit the variation diminishing property; the curves are smoother than the polygon defined by the control points.
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[av_heading tag=’h2′ padding=’10’ heading=’Parametric Equation of a Bezier Curve’ color=” style=’blockquote modern-quote’ custom_font=” size=” subheading_active=” subheading_size=’15’ custom_class=” admin_preview_bg=” av-desktop-hide=” av-medium-hide=” av-small-hide=” av-mini-hide=” av-medium-font-size-title=” av-small-font-size-title=” av-mini-font-size-title=” av-medium-font-size=” av-small-font-size=” av-mini-font-size=”][/av_heading]
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Where,
- p(t) = any point falling on the Bezier curve
- Bi= ith control point of the Bezier curve
- n= degree of curve
- Jn,i(t)= blending function = C(n,i)ti(1-t)n-i where C(n,i) =n!/i!(n-i)!
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By using a series of Bezier control cages, tangent points can be stitched together and formed into a composite that resembles a curved drawing. This can be used for modeling anything that needs to be displayed or drawn in a curved/cursive fashion.
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Through stitching together tangent vector points with their contained Bezier curve, letters could be fashioned in cursive on Proposal Bot.
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[av_heading tag=’h1′ padding=’10’ heading=’References/Resources’ color=” style=” custom_font=” size=” subheading_active=” subheading_size=’15’ custom_class=” admin_preview_bg=” av-desktop-hide=” av-medium-hide=” av-small-hide=” av-mini-hide=” av-medium-font-size-title=” av-small-font-size-title=” av-mini-font-size-title=” av-medium-font-size=” av-small-font-size=” av-mini-font-size=”][/av_heading]
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