// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Approximate circular arc by a Bézier curve" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
</jsxgraph>
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Approximate circular arc by a Bézier curve" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: false,
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
// Create circle through D with center M and to gliders A and B
var M = board.create('point', [0, 0], {
name: 'M'
});
var C = board.create('point', [0, -1], {
name: 'D'
});
var c = board.create('circle', [M, C], {
strokeWidth: 1
});
var A = board.create('glider', [1, 0, c], {
name: 'A'
});
var B = board.create('glider', [0, 1, c], {
name: 'B'
});
// Determine two optimal control points
var k = function(M, A, B) {
var ax = A.X() - M.X(),
ay = A.Y() - M.Y(),
bx = B.X() - M.X(),
by = B.Y() - M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax + bx) * (ax + bx) + (ay + by) * (ay + by));
if (JXG.Math.Geometry.rad(A, M, B) > Math.PI) {
d *= -1;
}
if (Math.abs(by - ay) > JXG.Math.eps) {
return (ax + bx) * (r / d - 0.5) * 8.0 / 3.0 / (by - ay);
} else {
return (ay + by) * (r / d - 0.5) * 8.0 / 3.0 / (ax - bx);
}
};
var P1 = board.create('point', [
() => A.X() - k(M, A, B) * (A.Y() - M.Y()),
() => A.Y() + k(M, A, B) * (A.X() - M.X())
], {
color: 'blue'
});
var P2 = board.create('point', [
() => B.X() + k(M, A, B) * (B.Y() - M.Y()),
() => B.Y() - k(M, A, B) * (B.X() - M.X())
], {
color: 'blue'
});
// Create the Bezier segment
var b = board.create('curve', JXG.Math.Numerics.bezier([A, P1, P2, B]), {
strokecolor: 'black',
strokeOpacity: 1,
strokeWidth: 3
});
var l1 = board.create('segment', [A, P1], {
dash: 2
});
var l2 = board.create('segment', [B, P2], {
dash: 2
});
</jsxgraph>