math - how to transform a sphere to a hemisphere, smoothly -

-

i using 3rd-party "rotator" object, providing smooth, random rotation along surface of sphere. rotator used control camera (see rotator.h/c in source code xscreensaver).

the output of rotator latitude , longitude. want camera stay above "equator" - limited hemisphere.

i'd rather not modify rotator itself. take latitude output , use absolute value of it. however, smooth rotator movement across equator not produce smooth camera motion: bounce.

i suppose scale output latitude rotator current range target range: e.g. f(lat) = (lat+1)/2 map (0, 1) range (0.5, 1). i.e. map whole "globe" northern hemisphere. movement still smooth. intended "south pole" rotator become "equator" camera. wouldn't result in strange motion? maybe discontinuities? i'm not sure.

is there way map sphere (latitude , longitude) hemisphere, smoothly?

update:

thanks attention , responses. couple of people have asked clarification on "smooth". mean not jerky: small change in velocity of rotator should mapped small change in velocity of camera. if took absolute value of latitude, 0 change in velocity of rotator crossed equator translate abrupt sign-flip of velocity of camera (a.k.a. bounce).

iirc equivalent requiring first derivative of velocity continuous. continuous second derivative might nice don't think it's essential.

the velocity derivative of position. "mirroring" lat value, create "corner" in position function when hitting equator. so, in order smooth transition, need map linear position (i.e, latitude function of time) function changes near equator, , 1st derivative 0 @ equator.

tom10's suggestion mapping lat'(lat) = (lat)^2 example of such function. however, need normalize result lat'(90deg) = 90deg. so, correct mapping should be:

lat'(lat) = 90*(lat/90)^2

an alternative parabole sin() function, appropriate shifting , normalizing. depending on how want velocity close original velocity when "away" equator, can have higher or lower order exponent values, like:

lat'(lat) = 90*( |lat| / 90)^k


Comments

Post a Comment

Popular posts from this blog

ASP.NET/SQL find the element ID and update database -

-
basically i've got update query runs when click submit button. i have asp:repeater in page layer inside this <asp:repeater id="dgbookings" runat="server" onitemdatabound="itemdb"> <itemtemplate> <div class="bookingscontent"> <div class="bookingdetails" id="<%# databinder.eval(container.dataitem, "booking_ref") %>"> <p class="infotext"><%# databinder.eval(container.dataitem, "adults") %> <asp:linkbutton onclick="editdetails" text="edit..." runat="server"></asp:linkbutton></p> <p class="infotext"><asp:linkbutton onclick="submitdetails" text="submit..." runat="server"></asp:linkbutton></p> </div> </div> </itemtemplate> <asp:repeater> and outputs ...
Read more

c++ - Compiling static TagLib 1.6.3 libraries for Windows -

-
i having super hard time compiling , using taglib 1.6.3 in qt project. i've tried can think of. taglib claims supported through cmake i'm not having luck. furthermore, i'm confused kinds of files need qt libs! i've built *.a files, *.lib, , *.dll. understand far... believe since i'm working in windows *.lib want. no matter do, end "undefined references" taglib functions try use when try compile qt project. have tried mingw32, msys, visual studio 2008, , cross-compiling windows on linux. turning nothing. what makes less sense me if compile same taglib source qt on mac (g++ think?) works fine! somewhere in windows compilation procedures have going wrong. have been smacking face on desk 30 (on , off) hours trying figure out. since qt uses mingw must compile taglib same compiler? if compile *.lib's visual studio not compatible? are *.a libraries usable in windows? (assuming mingw) i'm still trying handle on c++ stuff, after reading coun...
Read more

PostgreSQL 9.x - pg_read_binary_file & inserting files into bytea -

-
i have been looking everywhere (google, stackoverflow, etc.) documentation on how use postgresql pg_read_binary_file() function. the meaningful thing can find this page in official documentation. every time try use function error. for example: select pg_read_binary_file('/some/path/and/file.gif'); error: absolute path not allowed or select pg_read_binary_file('file.gif'); error: not stat file "file.gif": no such file or directory do need have file in specific directory postgres have access it? if directory? if matters, reason looking @ function because trying insert file database without doing crazy things . as stated @a_horse_with_no_name , @guedes solution ensure file being uploaded on server in pgdata directory. the postgres documentation state file location requirement. additionally, made symlink directory pgdata directory not disturb of postgres data structure. seems working , don't have of above...
Read more