Camera transition matrix - perspective
$begingroup$
Let's suppose:
1) $XY$ plane is perpendicular to the surface of the street given by an area between the two green lines and a normal to this plane has the same "direction" as the yellow line,
2) $XY$ has only three degrees of freedom - moving along $X$, $Y$, $Z$ ($Z$ is $X$ x $Y$),
3) a limit for an $X$- along translation is when $P1$ is coincident to $P2$.
How does the $theta$ change while translating by an $[x,y,z]$ vector? How would it change if I added a rotation along any of the given axes and got rid of the point $3)$ (6 degrees of freedom)? Can you give me any hint where to look for an answer?
Hope everything is clear!
matrices
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
$endgroup$
add a comment |
$begingroup$
Let's suppose:
1) $XY$ plane is perpendicular to the surface of the street given by an area between the two green lines and a normal to this plane has the same "direction" as the yellow line,
2) $XY$ has only three degrees of freedom - moving along $X$, $Y$, $Z$ ($Z$ is $X$ x $Y$),
3) a limit for an $X$- along translation is when $P1$ is coincident to $P2$.
How does the $theta$ change while translating by an $[x,y,z]$ vector? How would it change if I added a rotation along any of the given axes and got rid of the point $3)$ (6 degrees of freedom)? Can you give me any hint where to look for an answer?
Hope everything is clear!
matrices
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
$endgroup$
add a comment |
$begingroup$
Let's suppose:
1) $XY$ plane is perpendicular to the surface of the street given by an area between the two green lines and a normal to this plane has the same "direction" as the yellow line,
2) $XY$ has only three degrees of freedom - moving along $X$, $Y$, $Z$ ($Z$ is $X$ x $Y$),
3) a limit for an $X$- along translation is when $P1$ is coincident to $P2$.
How does the $theta$ change while translating by an $[x,y,z]$ vector? How would it change if I added a rotation along any of the given axes and got rid of the point $3)$ (6 degrees of freedom)? Can you give me any hint where to look for an answer?
Hope everything is clear!
matrices
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
$endgroup$
Let's suppose:
1) $XY$ plane is perpendicular to the surface of the street given by an area between the two green lines and a normal to this plane has the same "direction" as the yellow line,
2) $XY$ has only three degrees of freedom - moving along $X$, $Y$, $Z$ ($Z$ is $X$ x $Y$),
3) a limit for an $X$- along translation is when $P1$ is coincident to $P2$.
How does the $theta$ change while translating by an $[x,y,z]$ vector? How would it change if I added a rotation along any of the given axes and got rid of the point $3)$ (6 degrees of freedom)? Can you give me any hint where to look for an answer?
Hope everything is clear!
matrices
matrices
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
asked Dec 23 '18 at 18:11
Filip WichrowskiFilip Wichrowski
206
206
add a comment |
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%2f3050578%2fcamera-transition-matrix-perspective%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%2f3050578%2fcamera-transition-matrix-perspective%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
