Mixing
Iterative algorithm to draw an ellipse on sphere
$begingroup$
I am trying to understand a formula in the drawEllipse function of KDE Marble. This function draws an ellipse, given a center and height and width (in degrees). The algorithm draws upper and lower halves of the ellipse by constructing 2 polygons. Each of the polygons have precision number of points. Larger precision results in more precise ellipse formation. It iterates $tin [0dots p]$ where $p$ is the precision. For each such $t$ it creates a latitude longitude pair $(phi(t), lambda(t))$. Then it joins all these coordinates to form a polygon.
$$phi(t) = phipmfrac{h}{2}sqrt{1-t^{2}}$$
$$lambda(t) = lambda+frac{w}{2}t$$
Where $phi$ and $lambda$ are the latitude and longitude of the center. $h, w$ are width and height of the ellipse expressed in degrees. I don't understand why this works. I am trying to find a reference to this formula.
algorithms spherical-coordinates spherical-trigonometry
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
$endgroup$
add a comment |
$begingroup$
I am trying to understand a formula in the drawEllipse function of KDE Marble. This function draws an ellipse, given a center and height and width (in degrees). The algorithm draws upper and lower halves of the ellipse by constructing 2 polygons. Each of the polygons have precision number of points. Larger precision results in more precise ellipse formation. It iterates $tin [0dots p]$ where $p$ is the precision. For each such $t$ it creates a latitude longitude pair $(phi(t), lambda(t))$. Then it joins all these coordinates to form a polygon.
$$phi(t) = phipmfrac{h}{2}sqrt{1-t^{2}}$$
$$lambda(t) = lambda+frac{w}{2}t$$
Where $phi$ and $lambda$ are the latitude and longitude of the center. $h, w$ are width and height of the ellipse expressed in degrees. I don't understand why this works. I am trying to find a reference to this formula.
algorithms spherical-coordinates spherical-trigonometry
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
$endgroup$
add a comment |
$begingroup$
I am trying to understand a formula in the drawEllipse function of KDE Marble. This function draws an ellipse, given a center and height and width (in degrees). The algorithm draws upper and lower halves of the ellipse by constructing 2 polygons. Each of the polygons have precision number of points. Larger precision results in more precise ellipse formation. It iterates $tin [0dots p]$ where $p$ is the precision. For each such $t$ it creates a latitude longitude pair $(phi(t), lambda(t))$. Then it joins all these coordinates to form a polygon.
$$phi(t) = phipmfrac{h}{2}sqrt{1-t^{2}}$$
$$lambda(t) = lambda+frac{w}{2}t$$
Where $phi$ and $lambda$ are the latitude and longitude of the center. $h, w$ are width and height of the ellipse expressed in degrees. I don't understand why this works. I am trying to find a reference to this formula.
algorithms spherical-coordinates spherical-trigonometry
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
$endgroup$
I am trying to understand a formula in the drawEllipse function of KDE Marble. This function draws an ellipse, given a center and height and width (in degrees). The algorithm draws upper and lower halves of the ellipse by constructing 2 polygons. Each of the polygons have precision number of points. Larger precision results in more precise ellipse formation. It iterates $tin [0dots p]$ where $p$ is the precision. For each such $t$ it creates a latitude longitude pair $(phi(t), lambda(t))$. Then it joins all these coordinates to form a polygon.
$$phi(t) = phipmfrac{h}{2}sqrt{1-t^{2}}$$
$$lambda(t) = lambda+frac{w}{2}t$$
Where $phi$ and $lambda$ are the latitude and longitude of the center. $h, w$ are width and height of the ellipse expressed in degrees. I don't understand why this works. I am trying to find a reference to this formula.
algorithms spherical-coordinates spherical-trigonometry
algorithms spherical-coordinates spherical-trigonometry
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
edited Dec 22 '18 at 19:59
Neel Basu
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
asked Dec 22 '18 at 19:36
Neel BasuNeel Basu
201110
201110
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Ok, so I created the source code in question.
The drawEllipse method just draws an ellipse in carthesian coordinates, so on a sphere it will look skewed and will not resemble a real ellipse (unless the extent is very very small).
The formula used there is just the regular formula for an ellipse.
https://en.wikipedia.org/wiki/Ellipse#Equation
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3049776%2fiterative-algorithm-to-draw-an-ellipse-on-sphere%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Ok, so I created the source code in question.
The drawEllipse method just draws an ellipse in carthesian coordinates, so on a sphere it will look skewed and will not resemble a real ellipse (unless the extent is very very small).
The formula used there is just the regular formula for an ellipse.
https://en.wikipedia.org/wiki/Ellipse#Equation
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
$endgroup$
add a comment |
$begingroup$
Ok, so I created the source code in question.
The drawEllipse method just draws an ellipse in carthesian coordinates, so on a sphere it will look skewed and will not resemble a real ellipse (unless the extent is very very small).
The formula used there is just the regular formula for an ellipse.
https://en.wikipedia.org/wiki/Ellipse#Equation
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
$endgroup$
add a comment |
$begingroup$
Ok, so I created the source code in question.
The drawEllipse method just draws an ellipse in carthesian coordinates, so on a sphere it will look skewed and will not resemble a real ellipse (unless the extent is very very small).
The formula used there is just the regular formula for an ellipse.
https://en.wikipedia.org/wiki/Ellipse#Equation
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
$endgroup$
Ok, so I created the source code in question.
The drawEllipse method just draws an ellipse in carthesian coordinates, so on a sphere it will look skewed and will not resemble a real ellipse (unless the extent is very very small).
The formula used there is just the regular formula for an ellipse.
https://en.wikipedia.org/wiki/Ellipse#Equation
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
answered Jan 8 at 10:52
Torsten rahnTorsten rahn
1
1
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3049776%2fiterative-algorithm-to-draw-an-ellipse-on-sphere%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
