rotate 3d unit vector a, on plane of a and the j (up) axis The 2019 Stack Overflow Developer Survey Results Are InComponents of a 3d vector given specific anglesRotate Existing Vectortesting parallelity/perpendicularity of two 3D vectors with lengths close to zero using dot productFinding the exact value of the sine of the angle between a line and a planeFinding the angle between two 3 dimensional vectorsDerivative in Vector vs Index NotationReflect a ray off a circle so it hits another pointRotating an N-dimensional vector in a planeThe simplest billiards problemUnit vector of a planeRotate vector by angles between a unit vector and the positive x axis
Cooking pasta in a water boiler
Correct punctuation for showing a character's confusion
If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?
What do these terms in Caesar's Gallic wars mean?
writing variables above the numbers in tikz picture
Output the Arecibo Message
Did any laptop computers have a built-in 5 1/4 inch floppy drive?
Why don't hard Brexiteers insist on a hard border to prevent illegal immigration after Brexit?
Is it okay to consider publishing in my first year of PhD?
Why “相同意思的词” is called “同义词” instead of "同意词"？
How do you keep chess fun when your opponent constantly beats you?
Is bread bad for ducks?
Can withdrawing asylum be illegal?
Likelihood that a superbug or lethal virus could come from a landfill
What do hard-Brexiteers want with respect to the Irish border?
Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?
Keeping a retro style to sci-fi spaceships?
Are there any other methods to apply to solving simultaneous equations?
How to obtain a position of last non-zero element
Why are there uneven bright areas in this photo of black hole?
Can a flute soloist sit?
What's the name of these plastic connectors
Is Astrology considered scientific?
What is this sharp, curved notch on my knife for?
rotate 3d unit vector a, on plane of a and the j (up) axis
The 2019 Stack Overflow Developer Survey Results Are InComponents of a 3d vector given specific anglesRotate Existing Vectortesting parallelity/perpendicularity of two 3D vectors with lengths close to zero using dot productFinding the exact value of the sine of the angle between a line and a planeFinding the angle between two 3 dimensional vectorsDerivative in Vector vs Index NotationReflect a ray off a circle so it hits another pointRotating an N-dimensional vector in a planeThe simplest billiards problemUnit vector of a planeRotate vector by angles between a unit vector and the positive x axis
$begingroup$
vector $tilde a = ctilde i+dtilde j+etilde k$ is our input, and vector $tilde b = ftilde i+gtilde j+htilde k$ is our output, and $theta$ is the angle to rotate by. Essentially $tilde b = f(tilde a, theta)$
This is similar to Components of a 3d vector given specific angles, but I need to rotate the vector on the plane created by $tilde a$ and $tilde j$.
I attempted to create a function by converting $tilde a$ to a 2d point on this plane:
$(x, y) = (sqrt1-d^2, d)$
converting to a polar coordinate, adding alpha, converting back to cartesian, and taking the $y$ component as the value for $g$:
$$g = sqrtd^2+sqrt1-d^2 times sinbigg(tan^-1Big(fracdsqrt1-d^2Big)bigg)$$
$$f = frac c timessqrt1-d^2 sqrtc^2+e^2$$
$$h = frac etimes fc$$
This formula produces unexpected results when given a value close to $pmtilde j$, eg. $f(0.174126tilde i+0.984723tilde j, frac -pi16)$ returns $g = 0.996584$ which is higher the input value of $d=0.984723$. The expected value is aproximately $g=0.779171$ (I think). Continuing to tilt the resulting $tilde b$ by $frac-pi16$, cases $g$ to aproach $0.996$ ish.
Can anyone spot my error, or find a better way of doing this?
vectors
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
$endgroup$
add a comment |
$begingroup$
vector $tilde a = ctilde i+dtilde j+etilde k$ is our input, and vector $tilde b = ftilde i+gtilde j+htilde k$ is our output, and $theta$ is the angle to rotate by. Essentially $tilde b = f(tilde a, theta)$
This is similar to Components of a 3d vector given specific angles, but I need to rotate the vector on the plane created by $tilde a$ and $tilde j$.
I attempted to create a function by converting $tilde a$ to a 2d point on this plane:
$(x, y) = (sqrt1-d^2, d)$
converting to a polar coordinate, adding alpha, converting back to cartesian, and taking the $y$ component as the value for $g$:
$$g = sqrtd^2+sqrt1-d^2 times sinbigg(tan^-1Big(fracdsqrt1-d^2Big)bigg)$$
$$f = frac c timessqrt1-d^2 sqrtc^2+e^2$$
$$h = frac etimes fc$$
This formula produces unexpected results when given a value close to $pmtilde j$, eg. $f(0.174126tilde i+0.984723tilde j, frac -pi16)$ returns $g = 0.996584$ which is higher the input value of $d=0.984723$. The expected value is aproximately $g=0.779171$ (I think). Continuing to tilt the resulting $tilde b$ by $frac-pi16$, cases $g$ to aproach $0.996$ ish.
Can anyone spot my error, or find a better way of doing this?
vectors
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
$endgroup$
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26
add a comment |
$begingroup$
vector $tilde a = ctilde i+dtilde j+etilde k$ is our input, and vector $tilde b = ftilde i+gtilde j+htilde k$ is our output, and $theta$ is the angle to rotate by. Essentially $tilde b = f(tilde a, theta)$
This is similar to Components of a 3d vector given specific angles, but I need to rotate the vector on the plane created by $tilde a$ and $tilde j$.
I attempted to create a function by converting $tilde a$ to a 2d point on this plane:
$(x, y) = (sqrt1-d^2, d)$
converting to a polar coordinate, adding alpha, converting back to cartesian, and taking the $y$ component as the value for $g$:
$$g = sqrtd^2+sqrt1-d^2 times sinbigg(tan^-1Big(fracdsqrt1-d^2Big)bigg)$$
$$f = frac c timessqrt1-d^2 sqrtc^2+e^2$$
$$h = frac etimes fc$$
This formula produces unexpected results when given a value close to $pmtilde j$, eg. $f(0.174126tilde i+0.984723tilde j, frac -pi16)$ returns $g = 0.996584$ which is higher the input value of $d=0.984723$. The expected value is aproximately $g=0.779171$ (I think). Continuing to tilt the resulting $tilde b$ by $frac-pi16$, cases $g$ to aproach $0.996$ ish.
Can anyone spot my error, or find a better way of doing this?
vectors
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
$endgroup$
vector $tilde a = ctilde i+dtilde j+etilde k$ is our input, and vector $tilde b = ftilde i+gtilde j+htilde k$ is our output, and $theta$ is the angle to rotate by. Essentially $tilde b = f(tilde a, theta)$
This is similar to Components of a 3d vector given specific angles, but I need to rotate the vector on the plane created by $tilde a$ and $tilde j$.
I attempted to create a function by converting $tilde a$ to a 2d point on this plane:
$(x, y) = (sqrt1-d^2, d)$
converting to a polar coordinate, adding alpha, converting back to cartesian, and taking the $y$ component as the value for $g$:
$$g = sqrtd^2+sqrt1-d^2 times sinbigg(tan^-1Big(fracdsqrt1-d^2Big)bigg)$$
$$f = frac c timessqrt1-d^2 sqrtc^2+e^2$$
$$h = frac etimes fc$$
This formula produces unexpected results when given a value close to $pmtilde j$, eg. $f(0.174126tilde i+0.984723tilde j, frac -pi16)$ returns $g = 0.996584$ which is higher the input value of $d=0.984723$. The expected value is aproximately $g=0.779171$ (I think). Continuing to tilt the resulting $tilde b$ by $frac-pi16$, cases $g$ to aproach $0.996$ ish.
Can anyone spot my error, or find a better way of doing this?
vectors
vectors
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
asked Mar 24 at 4:59
Alice JackaAlice Jacka
61
61
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26
add a comment |
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26
add a comment |
0
active
oldest
votes
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%2f3160117%2frotate-3d-unit-vector-a-on-plane-of-a-and-the-j-up-axis%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3160117%2frotate-3d-unit-vector-a-on-plane-of-a-and-the-j-up-axis%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
$begingroup$
Find the angle of rotation by dot multiplication. Why moving to 2D?
$endgroup$
– Moti
Mar 24 at 6:32
$begingroup$
@Moti because f and h can be found from a and g, and 2d allowed me to use radial coordinates which (I think) did exactly what I want, just in 2d
$endgroup$
– Alice Jacka
Mar 24 at 7:05
$begingroup$
@Moti could you elaborate on the dot multiplication?
$endgroup$
– Alice Jacka
Mar 24 at 7:26