Problem 46963. Roots, Bloody Roots: part 2/2

Created by Rafael S.T. Vieira

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Using curves or lines, we can easily spot roots from n-degree polynomials in 2D: wherever they cross the real line, we know there is a root. However, as we are well aware, roots can also be complex numbers. In this case, plotting curves no longer seem adequate since they won't be found at the real line. That's when coloring comes into place; by painting the 2D plane, we can visualize where complex or real roots are and get a sense of what's happening in a function.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>This problem is the second part of a previous one; if you haven't solved it, </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46833-roots-bloody-roots-part-1-2\"><w:r><w:t>Problem 46833</w:t></w:r></w:hyperlink><w:r><w:t>, please do it before proceeding. Finally, we will color the complex plane following the roots of any given polynomial using the color space HSV. The same rules for HSV-space apply, but instead of using the cube root for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>V</w:t></w:r></w:customXml><w:r><w:t>, we will allow the user to choose its </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Gamma_correction\"><w:r><w:t>gamma correction</w:t></w:r></w:hyperlink><w:r><w:t> parameters used to the</w:t></w:r><w:hyperlink w:docLocation=\"https://www.codecademy.com/articles/normalization#:~:text=Min%2Dmax%20normalization%20is%20one,decimal%20between%200%20and%201.\"><w:r><w:t> Min-max normalization</w:t></w:r></w:hyperlink><w:r><w:t> of the distance, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>V = A\\sqrt[\\gamma]{\\frac{\\beta-\\min(\\beta)}{\\max(\\beta)-\\min(\\beta)}}</w:t></w:r></w:customXml><w:r><w:t> , in which </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A \\in \\mathbb{R} </w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>0 \\le \\gamma \\le 1, ~\\gamma\\in\\mathbb{R}</w:t></w:r></w:customXml><w:r><w:t>. Once the three values are computed, convert them to RGB space using the function </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>hsv2rgb </w:t></w:r><w:r><w:t>and</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>round them to 4 decimal places</w:t></w:r><w:r><w:t>. Moreover, instead of plotting a matrix, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:t> x </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> x 3, centered at the origin, we will center it at the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Minimum_bounding_box\"><w:r><w:t>bounding-box</w:t></w:r></w:hyperlink><w:r><w:t> enveloping the roots of a given polynomial </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P</w:t></w:r></w:customXml><w:r><w:t>; horizontal axis imaginary and vertical axis real. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Any line has only one root, which should always be at the center of the image (generating a figure similar to those obtained at the previous problem). As another example of expected output, this is the result for the 10th roots of unit given </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P=[1,0,0,0,0,0,0,0,0,0,-1]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\gamma=0.1</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A=2</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m=400</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n = 400</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"508\"/><w:attr w:name=\"width\" w:val=\"574\"/><w:attr w:name=\"verticalAlign\" w:val=\"middle\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Polynomials may have any number of roots between 1 and the maximum that MATLAB can compute (or Cody), which means one or two dimensions may have thickness 0. Your algorithm must take this case into account by calculating the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Minimum_bounding_box\"><w:r><w:t>minimum bounding-box</w:t></w:r></w:hyperlink><w:r><w:t> and doubling the distance from the box's center to its edges. If one size has thickness zero, use the same thickness as the non-zero one, and if both are zero, use a square of side 2 (a distance of two times one). The center of the box can be found using </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\left ( \\frac{\\min(a)+\\max(a)} {2}, \\frac{\\min(b)+\\max(b)} {2} \\right )</w:t></w:r></w:customXml><w:r><w:t>, in which </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a+bi \\in \\mathbb{C}</w:t></w:r></w:customXml><w:r><w:t>. Since we render a matrix of size </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:t>x</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>, your algorithm should convert each pixel position to the complex roots' </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Minimum_bounding_box\"><w:r><w:t>bounding box</w:t></w:r></w:hyperlink><w:r><w:t> interval. This operation is linear, and you may use the function</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> interp1.</w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t> All values obtained by interpolation must also be rounded to 4 decimal places.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Good luck!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Note-1:</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>This problem is inspired by a 3Blue1Brown's video: </w:t></w:r><w:hyperlink w:docLocation=\"https://www.youtube.com/watch?v=b7FxPsqfkOY\"><w:r><w:rPr><w:i/></w:rPr><w:t>https://www.youtube.com/watch?v=b7FxPsqfkOY</w:t></w:r></w:hyperlink><w:r><w:rPr><w:i/></w:rPr><w:t>, and I recommend that you watch his video if you haven't already. However, it is not required that you do to solve this problem.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Note-2:</w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t> This problem was last updated 22/08/2020. Thanks to Svyatoslav's feedback. Please, let me know if anyone run into issues. 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<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 1209.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 604.9px; transform-origin: 407px 604.9px; vertical-align: baseline; "><div style="block-size: 83.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 41.6px; text-align: left; transform-origin: 384px 41.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Using curves or lines, we can easily spot roots from n-degree polynomials in 2D: wherever they cross the real line, we know there is a root. However, as we are well aware, roots can also be complex numbers. In this case, plotting curves no longer seem adequate since they won't be found at the real line. That's when coloring comes into place; by painting the 2D plane, we can visualize where complex or real roots are and get a sense of what's happening in a function.</div><div style="block-size: 171px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 85.5px; text-align: left; transform-origin: 384px 85.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">This problem is the second part of a previous one; if you haven't solved it, <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46833-roots-bloody-roots-part-1-2">Problem 46833</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, please do it before proceeding. Finally, we will color the complex plane following the roots of any given polynomial using the color space HSV. The same rules for HSV-space apply, but instead of using the cube root for V<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, we will allow the user to choose its <a target='_blank' href = "https://en.wikipedia.org/wiki/Gamma_correction">gamma correction</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> parameters used to the<a target='_blank' href = "https://www.codecademy.com/articles/normalization#:~:text=Min%2Dmax%20normalization%20is%20one,decimal%20between%200%20and%201."> Min-max normalization</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> of the distance, <img 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src="data:image/png;base64,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" width="43.5" height="17.5" style="width: 43.5px; height: 17.5px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,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" width="109.5" height="17.5" style="width: 109.5px; height: 17.5px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. Once the three values are computed, convert them to RGB space using the function <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">hsv2rgb <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">and<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">round them to 4 decimal places<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. Moreover, instead of plotting a matrix, m<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> x n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> x 3, centered at the origin, we will center it at the <a target='_blank' href = "https://en.wikipedia.org/wiki/Minimum_bounding_box">bounding-box</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> enveloping the roots of a given polynomial P<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">; horizontal axis imaginary and vertical axis real. </div><div style="block-size: 62.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.2px; text-align: left; transform-origin: 384px 31.2px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Any line has only one root, which should always be at the center of the image (generating a figure similar to those obtained at the previous problem). As another example of expected output, this is the result for the 10th roots of unit given <img 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" data-image-state="image-loaded"></div><div style="block-size: 158.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 79.3px; text-align: left; transform-origin: 384px 79.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Polynomials may have any number of roots between 1 and the maximum that MATLAB can compute (or Cody), which means one or two dimensions may have thickness 0. Your algorithm must take this case into account by calculating the <a target='_blank' href = "https://en.wikipedia.org/wiki/Minimum_bounding_box">minimum bounding-box</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> and doubling the distance from the box's center to its edges. If one size has thickness zero, use the same thickness as the non-zero one, and if both are zero, use a square of side 2 (a distance of two times one). The center of the box can be found using <img src="data:image/png;base64,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" width="242" height="34" style="width: 242px; height: 34px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, in which <img src="data:image/png;base64,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" width="68.5" height="17.5" style="width: 68.5px; height: 17.5px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. Since we render a matrix of size m<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">xn<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, your algorithm should convert each pixel position to the complex roots' <a target='_blank' href = "https://en.wikipedia.org/wiki/Minimum_bounding_box">bounding box</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> interval. This operation is linear, and you may use the function<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> interp1.<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> All values obtained by interpolation must also be rounded to 4 decimal places.</div><div style="block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "></div><div style="block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Good luck!</div><div style="block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "></div><div style="block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Note-1:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">This problem is inspired by a 3Blue1Brown's video: <a target='_blank' href = "https://www.youtube.com/watch?v=b7FxPsqfkOY">https://www.youtube.com/watch?v=b7FxPsqfkOY</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, and I recommend that you watch his video if you haven't already. However, it is not required that you do to solve this problem.</div><div style="block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Note-2:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> This problem was last updated 22/08/2020. Thanks to Svyatoslav's feedback. Please, let me know if anyone run into issues. </div></div></div>

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7 Solutions
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Last Solution submitted on Mar 08, 2021

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Svyatoslav Golousov on 21 Oct 2020

My solution passes first and last tests, but fails others, could you take a look, please?

Rafael S.T. Vieira on 22 Oct 2020

No problem, Svyatoslav, I will take a look tomorrow.

Rafael S.T. Vieira on 22 Oct 2020

Hi, Svyatoslav, I've figured out what the problem was. It appears there is a small error < 1e-10 between our interpolation methods. This error wouldn't matter regularly, but since we are doing gamma correction, that error gets magnified. To fix this, I've changed the problem description to request that all interpolations be rounded to 4 decimal places. This seems to resolve the issue (since there will be no error to be magnified by the gamma correction).

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Solution 3314043

3 Comments

3 Comments

Rafael S.T. Vieira on 22 Oct 2020

If you round both results from linspace to 4 decimal places, this solution will pass the test suite.

Svyatoslav Golousov on 22 Oct 2020

Helped, thank you!

Rafael S.T. Vieira on 22 Oct 2020

No problem. And congratulations :)

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bounding-box coloring complex plane gamma-correction hsv2rgb interp1 roots

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Problem 46963. Roots, Bloody Roots: part 2/2

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Problem 46963. Roots, Bloody Roots: part 2/2

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