File:Circle and cubic bezier.svg
Summary
Cubic <a href="https://en.wikipedia.org/wiki/B%C3%A9zier_spline" class="extiw" title="w:Bézier spline">Bézier spline</a> approximation (in red) overlayed on a black circle of radius 112 units, with tangent (on-curve) control points drawn as squares and off-curve control points drawn as circles. The spline's on-curve control points are placed at the circle's horizontal and vertical tangent points. Off-curve control points are placed on these tangent lines, <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e50bcd40900219ebc49514dc1090d69c9cd611c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -2.505ex; width:49.92ex; height:6.176ex;" alt="{\displaystyle {\frac {4}{3}}\left({\frac {1-\cos 45^{\circ }}{\sin 45^{\circ }}}\right)\times 112={\frac {4}{3}}({\sqrt {2}}-1)\times 112=62}"> units from the on-curve control points.
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:04, 16 January 2017 | | 256 × 256 (1 KB) | 127.0.0.1 (talk) | Cubic <a href="https://en.wikipedia.org/wiki/B%C3%A9zier_spline" class="extiw" title="w:Bézier spline">Bézier spline</a> approximation (in red) overlayed on a black circle of radius 112 units, with tangent (on-curve) control points drawn as squares and off-curve control points drawn as circles. The spline's on-curve control points are placed at the circle's horizontal and vertical tangent points. Off-curve control points are placed on these tangent lines, <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>4</mn><mn>3</mn></mfrac></mrow><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mn>1</mn><mo>−<!-- − --></mo><mi>cos</mi><mo><!-- --></mo><msup><mn>45</mn><mrow class="MJX-TeXAtom-ORD"><mo>∘<!-- ∘ --></mo></mrow></msup></mrow><mrow><mi>sin</mi><mo><!-- --></mo><msup><mn>45</mn><mrow class="MJX-TeXAtom-ORD"><mo>∘<!-- ∘ --></mo></mrow></msup></mrow></mfrac></mrow><mo>)</mo></mrow><mo>×<!-- × --></mo><mn>112</mn><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>4</mn><mn>3</mn></mfrac></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow><mo>−<!-- − --></mo><mn>1</mn><mo stretchy="false">)</mo><mo>×<!-- × --></mo><mn>112</mn><mo>=</mo><mn>62</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\frac {4}{3}}\left({\frac {1-\cos 45^{\circ }}{\sin 45^{\circ }}}\right)\times 112={\frac {4}{3}}({\sqrt {2}}-1)\times 112=62}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e50bcd40900219ebc49514dc1090d69c9cd611c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -2.505ex; width:49.92ex; height:6.176ex;" alt="{\displaystyle {\frac {4}{3}}\left({\frac {1-\cos 45^{\circ }}{\sin 45^{\circ }}}\right)\times 112={\frac {4}{3}}({\sqrt {2}}-1)\times 112=62}"></span> units from the on-curve control points. |
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