Plotting points on a halfcircle, given diameter and facing direction.
$begingroup$
I know the coordinates of point $1$ and $2$ and some radius $r$ at a halfcircle with centerpoint point $1$, with the gap of the halfcircle pointing towards point $2$. How do I compute the (lets say $10$) points that the halfcircle contains of? Also how do I compute the intersecting point between a line segment following the halfcircle and a line segment lying horizontally towards point $1$, at point $2$.
(radius $r$, ($x1,y1$), ($x2,y2$) are known)
See below for an example
geometry trigonometry euclidean-geometry circle polygons
edited Dec 6 '18 at 9:24
Math Girl
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
$endgroup$
add a comment |
$begingroup$
I know the coordinates of point $1$ and $2$ and some radius $r$ at a halfcircle with centerpoint point $1$, with the gap of the halfcircle pointing towards point $2$. How do I compute the (lets say $10$) points that the halfcircle contains of? Also how do I compute the intersecting point between a line segment following the halfcircle and a line segment lying horizontally towards point $1$, at point $2$.
(radius $r$, ($x1,y1$), ($x2,y2$) are known)
See below for an example
geometry trigonometry euclidean-geometry circle polygons
edited Dec 6 '18 at 9:24
Math Girl
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
$endgroup$
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54
add a comment |
$begingroup$
I know the coordinates of point $1$ and $2$ and some radius $r$ at a halfcircle with centerpoint point $1$, with the gap of the halfcircle pointing towards point $2$. How do I compute the (lets say $10$) points that the halfcircle contains of? Also how do I compute the intersecting point between a line segment following the halfcircle and a line segment lying horizontally towards point $1$, at point $2$.
(radius $r$, ($x1,y1$), ($x2,y2$) are known)
See below for an example
geometry trigonometry euclidean-geometry circle polygons
edited Dec 6 '18 at 9:24
Math Girl
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
$endgroup$
I know the coordinates of point $1$ and $2$ and some radius $r$ at a halfcircle with centerpoint point $1$, with the gap of the halfcircle pointing towards point $2$. How do I compute the (lets say $10$) points that the halfcircle contains of? Also how do I compute the intersecting point between a line segment following the halfcircle and a line segment lying horizontally towards point $1$, at point $2$.
(radius $r$, ($x1,y1$), ($x2,y2$) are known)
See below for an example
geometry trigonometry euclidean-geometry circle polygons
geometry trigonometry euclidean-geometry circle polygons
edited Dec 6 '18 at 9:24
Math Girl
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
edited Dec 6 '18 at 9:24
Math Girl
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
edited Dec 6 '18 at 9:24
Math Girl
631318
edited Dec 6 '18 at 9:24
Math Girl
631318
edited Dec 6 '18 at 9:24
Math Girl
631318
631318
asked Dec 6 '18 at 9:21
user3107438user3107438
255
asked Dec 6 '18 at 9:21
user3107438user3107438
255
asked Dec 6 '18 at 9:21
user3107438user3107438
255
255
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54
add a comment |
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
A polar coordinate system could be combined with the slope formula and the distance formula. Or use a land surveying system:
Point 2 to Point 1 is InvTan((x1 - x2) / (y1 - y2)) .
Then for a direction in a four-quadrant system, if (x1 - x2) is positive that is East else West. And if (y1 - y2) is positive then that is North else South.
Then determine the forward direction 90 degrees off the calculated direction at Point 1 and forward a point at distance r.
Forward y = (Cos(ForwardDirection) * r) + y1 .
Forward x = (Sin(ForwardDirection) * r) + x1 .
If the ForwardDirection is North then the value added to y1 is positive else negative if South.
If the ForwardDirection is East then the value added to x1 is positive else negative if West.
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
$endgroup$
add a comment |
$begingroup$
Find the equation of the line $(L_1)$ joining the two given points, and find the point of intersection of the line with the circle.
To calculate the intersection point, find the line $L_d$ perpendicular to $(L_1)$ and passing through the point $(P_1)$. Find the two end points $P_3,P_4$ of the diameter of the semicircle. Make lines $L_3,L_4$ through them parallel to $L_1$.
Find the line through $P_2$ parallel to $L_d$. intersection of $L_d$ with $L_3$ and $L_4$ are the required points.
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
$endgroup$
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%2f3028258%2fplotting-points-on-a-halfcircle-given-diameter-and-facing-direction%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A polar coordinate system could be combined with the slope formula and the distance formula. Or use a land surveying system:
Point 2 to Point 1 is InvTan((x1 - x2) / (y1 - y2)) .
Then for a direction in a four-quadrant system, if (x1 - x2) is positive that is East else West. And if (y1 - y2) is positive then that is North else South.
Then determine the forward direction 90 degrees off the calculated direction at Point 1 and forward a point at distance r.
Forward y = (Cos(ForwardDirection) * r) + y1 .
Forward x = (Sin(ForwardDirection) * r) + x1 .
If the ForwardDirection is North then the value added to y1 is positive else negative if South.
If the ForwardDirection is East then the value added to x1 is positive else negative if West.
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
$endgroup$
add a comment |
$begingroup$
A polar coordinate system could be combined with the slope formula and the distance formula. Or use a land surveying system:
Point 2 to Point 1 is InvTan((x1 - x2) / (y1 - y2)) .
Then for a direction in a four-quadrant system, if (x1 - x2) is positive that is East else West. And if (y1 - y2) is positive then that is North else South.
Then determine the forward direction 90 degrees off the calculated direction at Point 1 and forward a point at distance r.
Forward y = (Cos(ForwardDirection) * r) + y1 .
Forward x = (Sin(ForwardDirection) * r) + x1 .
If the ForwardDirection is North then the value added to y1 is positive else negative if South.
If the ForwardDirection is East then the value added to x1 is positive else negative if West.
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
$endgroup$
add a comment |
$begingroup$
A polar coordinate system could be combined with the slope formula and the distance formula. Or use a land surveying system:
Point 2 to Point 1 is InvTan((x1 - x2) / (y1 - y2)) .
Then for a direction in a four-quadrant system, if (x1 - x2) is positive that is East else West. And if (y1 - y2) is positive then that is North else South.
Then determine the forward direction 90 degrees off the calculated direction at Point 1 and forward a point at distance r.
Forward y = (Cos(ForwardDirection) * r) + y1 .
Forward x = (Sin(ForwardDirection) * r) + x1 .
If the ForwardDirection is North then the value added to y1 is positive else negative if South.
If the ForwardDirection is East then the value added to x1 is positive else negative if West.
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
$endgroup$
A polar coordinate system could be combined with the slope formula and the distance formula. Or use a land surveying system:
Point 2 to Point 1 is InvTan((x1 - x2) / (y1 - y2)) .
Then for a direction in a four-quadrant system, if (x1 - x2) is positive that is East else West. And if (y1 - y2) is positive then that is North else South.
Then determine the forward direction 90 degrees off the calculated direction at Point 1 and forward a point at distance r.
Forward y = (Cos(ForwardDirection) * r) + y1 .
Forward x = (Sin(ForwardDirection) * r) + x1 .
If the ForwardDirection is North then the value added to y1 is positive else negative if South.
If the ForwardDirection is East then the value added to x1 is positive else negative if West.
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
answered Dec 7 '18 at 1:34
S SpringS Spring
1723
1723
add a comment |
add a comment |
$begingroup$
Find the equation of the line $(L_1)$ joining the two given points, and find the point of intersection of the line with the circle.
To calculate the intersection point, find the line $L_d$ perpendicular to $(L_1)$ and passing through the point $(P_1)$. Find the two end points $P_3,P_4$ of the diameter of the semicircle. Make lines $L_3,L_4$ through them parallel to $L_1$.
Find the line through $P_2$ parallel to $L_d$. intersection of $L_d$ with $L_3$ and $L_4$ are the required points.
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
$endgroup$
add a comment |
$begingroup$
Find the equation of the line $(L_1)$ joining the two given points, and find the point of intersection of the line with the circle.
To calculate the intersection point, find the line $L_d$ perpendicular to $(L_1)$ and passing through the point $(P_1)$. Find the two end points $P_3,P_4$ of the diameter of the semicircle. Make lines $L_3,L_4$ through them parallel to $L_1$.
Find the line through $P_2$ parallel to $L_d$. intersection of $L_d$ with $L_3$ and $L_4$ are the required points.
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
$endgroup$
add a comment |
$begingroup$
Find the equation of the line $(L_1)$ joining the two given points, and find the point of intersection of the line with the circle.
To calculate the intersection point, find the line $L_d$ perpendicular to $(L_1)$ and passing through the point $(P_1)$. Find the two end points $P_3,P_4$ of the diameter of the semicircle. Make lines $L_3,L_4$ through them parallel to $L_1$.
Find the line through $P_2$ parallel to $L_d$. intersection of $L_d$ with $L_3$ and $L_4$ are the required points.
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
$endgroup$
Find the equation of the line $(L_1)$ joining the two given points, and find the point of intersection of the line with the circle.
To calculate the intersection point, find the line $L_d$ perpendicular to $(L_1)$ and passing through the point $(P_1)$. Find the two end points $P_3,P_4$ of the diameter of the semicircle. Make lines $L_3,L_4$ through them parallel to $L_1$.
Find the line through $P_2$ parallel to $L_d$. intersection of $L_d$ with $L_3$ and $L_4$ are the required points.
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
answered Dec 6 '18 at 10:00
Sri Krishna SahooSri Krishna Sahoo
606217
606217
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%2f3028258%2fplotting-points-on-a-halfcircle-given-diameter-and-facing-direction%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
$begingroup$
What do you mean "points" the half circle "contains-of"? integer points? any ten points lying on the semi-circumference? or points "inside" the semicircle?
$endgroup$
– Sri Krishna Sahoo
Dec 6 '18 at 9:54