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  • Raycasting tutorial / vector math question

    - by mattboy
    I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question. In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel from 1 x-side to the next x-side, or from 1 y-side to the next y-side, in the square grid that makes up the world map (see below screenshot). In the tutorial they are calculated as follows, but without much explanation: //length of ray from one x or y-side to next x or y-side double deltaDistX = sqrt(1 + (rayDirY * rayDirY) / (rayDirX * rayDirX)); double deltaDistY = sqrt(1 + (rayDirX * rayDirX) / (rayDirY * rayDirY)); rayDirY and rayDirX are the direction of a ray that has been cast. How do you get these formulas? It looks like pythagorean theorem is part of it, but somehow there's division involved here. Can anyone clue me in as to what mathematical knowledge I'm missing here, or "prove" the formula by showing how it's derived?

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  • How does a website like Mathway work?

    - by Bob
    I recently found a website called Mathway Basically, it works by allowing you to choose your "level of math" (which it uses to determine what tools it should provide to you) and then allows you to input a math problem which it then solves for you, and gives you detailed solutions (you have to try it, it's really cool). I was wondering how it worked on two levels. First off, how would they parse the math problem (and all the sometimes foreign mathematical operators)? How do they get from text to numbers, variables, and operators? Second, how do they generate the explanations? While you have to pay for the detailed solutions (which are explanations of how they solved the problem), I've seen their preview screenshots, and it looks very detailed. The explanations are given in full, accurate sentences. How would they generate something like that?

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  • Rotate a vector by given degrees (errors when value over 90)

    - by Ivan
    I created a function to rotate a vector by a given number of degrees. It seems to work fine when given values in the range -90 to +90. Beyond this, the amount of rotation decreases, i.e., I think objects are rotating the same amount for 80 and 100 degrees. I think this diagram might be a clue to my problem, but I don't quite understand what it's showing. Must I use a different trig function depending on the radians value? The programming examples I've been able to find look similar to mine (not varying the trig functions). Vector2D.prototype.rotate = function(angleDegrees) { var radians = angleDegrees * (Math.PI / 180); var ca = Math.cos(radians); var sa = Math.sin(radians); var rx = this.x*ca - this.y*sa; var ry = this.x*sa + this.y*ca; this.x = rx; this.y = ry; };

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  • Math behind multivariate testing for website optimization

    - by corkjack
    I am looking for theoretical resources (books, tutorials, etc.) to learn about making sound statistical inferences given (plenty of) multivariate website conversion data. I'm after the math involved, and cannot find any good non-marketing stuff on the web. The sort of questions I want to answer: how much impact does a single variable (e.g. color of text) have? what is the correlation between variables? what type of distribution is used for modelling (Gaussian, Binomial, etc.)? When using statistics to analyze results - what should be considered as a random variable - the web-page element that gets different variations or the binary conversion-or-no-conversion outcome of an impression? There's plenty of information about different website optimization testing methods and their benefits\pitfalls, plenty of information about multivariate statistics in general, do you guys know of resources that discuss statistics in this specific context of website optimization ? Thanks for any info!

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  • In 3D camera math, calculate what Z depth is pixel unity for a given FOV

    - by badweasel
    I am working in iOS and OpenGL ES 2.0. Through trial and error I've figured out a frustum to where at a specific z depth pixels drawn are 1 to 1 with my source textures. So 1 pixel in my texture is 1 pixel on the screen. For 2d games this is good. Of course it means that I also factor in things like the size of the quad and the size of the texture. For example if my sprite is a quad 32x32 pixels. The quad size is 3.2 units wide and tall. And the texcoords are 32 / the size of the texture wide and tall. Then the frustum is: matrixFrustum(-(float)backingWidth/frustumScale,(float)backingWidth/frustumScale, -(float)backingHeight/frustumScale, (float)backingHeight/frustumScale, 40, 1000, mProjection); Where frustumScale is 800 for a retina screen. Then at a distance of 800 from camera the sprite is pixel for pixel the same as photoshop. For 3d games sometimes I still want to be able to do this. But depending on the scene I sometimes need the FOV to be different things. I'm looking for a way to figure out what Z depth will achieve this same pixel unity for a given FOV. For this my mProjection is set using: matrixPerspective(cameraFOV, near, far, (float)backingWidth / (float)backingHeight, mProjection); With testing I found that at an FOV of 45.0 a Z of 38.5 is very close to pixel unity. And at an FOV of 30.0 a Z of 59.5 is about right. But how can I calculate a value that is spot on? Here's my matrixPerspecitve code: void matrixPerspective(float angle, float near, float far, float aspect, mat4 m) { //float size = near * tanf(angle / 360.0 * M_PI); float size = near * tanf(degreesToRadians(angle) / 2.0); float left = -size, right = size, bottom = -size / aspect, top = size / aspect; // Unused values in perspective formula. m[1] = m[2] = m[3] = m[4] = 0; m[6] = m[7] = m[12] = m[13] = m[15] = 0; // Perspective formula. m[0] = 2 * near / (right - left); m[5] = 2 * near / (top - bottom); m[8] = (right + left) / (right - left); m[9] = (top + bottom) / (top - bottom); m[10] = -(far + near) / (far - near); m[11] = -1; m[14] = -(2 * far * near) / (far - near); } And my mView is set using: lookAtMatrix(cameraPos, camLookAt, camUpVector, mView); * UPDATE * I'm going to leave this here in case anyone has a different solution, can explain how they do it, or why this works. This is what I figured out. In my system I use a 10th scale unit to pixels on non-retina displays and a 20th scale on retina displays. The iPhone is 640 pixels wide on retina and 320 pixels wide on non-retina (obsolete). So if I want something to be the full screen width I divide by 20 to get the OpenGL unit width. Then divide that by 2 to get the left and right unit position. Something 32 units wide centered on the screen goes from -16 to +16. Believe it or not I have an excel spreadsheet do all this math for me and output all the vertex data for my sprite sheet. It's an arbitrary thing I made up to do .1 units = 1 non-retina pixel or 2 retina pixels. I could have made it .01 units = 2 pixels and someday I might switch to that. But for now it's the other. So the width of the screen in units is 32.0, and that means the left most pixel is at -16.0 and the right most is at 16.0. After messing a bit I figured out that if I take the [0] value of an identity modelViewProjection matrix and multiply it by 16 I get the depth required to get 1:1 pixels. I don't know why. I don't know if the 16 is related to the screen size or just a lucky guess. But I did a test where I placed a sprite at that calculated depth and varied the FOV through all the valid values and the object stays steady on screen with 1:1 pixels. So now I'm just calculating the unityDepth that way. If someone gives me a better answer I'll checkmark it.

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  • Documenting mathematical logic in code

    - by Kiril Raychev
    Sometimes, although not often, I have to include math logic in my code. The concepts used are mostly very simple, but the resulting code is not - a lot of variables with unclear purpose, and some operations with not so obvious intent. I don't mean that the code is unreadable or unmaintainable, just that it's waaaay harder to understand than the actual math problem. I try to comment the parts which are hardest to understand, but there is the same problem as in just coding them - text does not have the expressive power of math. I am looking for a more efficient and easy to understand way of explaining the logic behind some of the complex code, preferably in the code itself. I have considered TeX - writing the documentation and generating it separately from the code. But then I'd have to learn TeX, and the documentation will not be in the code itself. Another thing I thought of is taking a picture of the mathematical notations, equations and diagrams written on paper/whiteboard, and including it in javadoc. Is there a simpler and clearer way? P.S. Giving descriptive names(timeOfFirstEvent instead of t1) to the variables actually makes the code more verbose and even harder too read.

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  • How do I become better in math, after being a programmer for several years.

    - by loxs
    I've had quite a weird career till now. First I graduated from a medical school. Then I went into marketing (pharmaceuticals). And then umm, after some time, I decided to go for my (till then) hobby and became a "professional" programmer. I've been quite successful at this ever since. I have quite some languages "under my belt". I earn not bad and I have been involved in the opensource community quite heavily. The thing is that I suck at math :). Well, not totally of course, as I get my work done. But I don't know how much I suck. And I don't know how to find out. Math has never really been of any priority during my middle/high school years. I only picked as little as I could afford, because I was always getting ready to go for Medicine. Of course I know the basics of algebra. Things like "normal" and square equations. Also the basics of geometry. But well, there are things that I have missed. And lately I am being fascinated by things like probability theory, infinity, chaos/order etc. But every time I try to learn something about these topics, I hit a wall of terminology, special symbols, and some special kind of thinking, that is quite like mine (a programmer), but also a lot different (and appears weird to me). So, what kinds of books would you recommend me? It's very hard to find something suitable. All that I find are either too easy (and boring) or totally impenetrable.

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  • Some date math fun

    - by drsql
    Note: This concept presented is pretty simple and I am not claiming that I am the first to do this… so if you were the one who came up with this, let me know and I will give you linkage Today I was needing to get the data for the current month for a query, and it hit me that I really didn’t have a good way to do this.  There were two common methods that people use: WHERE YEAR(MonthColumn) = YEAR(Getdate()) AND MONTH(MonthColumn) = MONTH(Getdate()) But this particular method is pretty horrible...(read more)

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  • Some date math fun

    - by drsql
    Note: This concept presented is pretty simple and I am not claiming that I am the first to do this… so if you were the one who came up with this, let me know and I will give you linkage Today I was needing to get the data for the current month for a query, and it hit me that I really didn’t have a good way to do this.  There were two common methods that people use: WHERE YEAR(MonthColumn) = YEAR(Getdate()) AND MONTH(MonthColumn) = MONTH(Getdate()) But this particular method is pretty horrible...(read more)

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  • as3 3D camera lookat

    - by Johannes Jensen
    I'm making a 3D camera scene in Flash, draw using drawTriangles() and rotated and translated using a Matrix3D. I've got the camera to look after a specific point, but only on the Y-axis, using the x and z coordinates, here is my code so far: var dx:Number = camera.x - lookAt.x; var dy:Number = camera.y - lookAt.y; var dz:Number = camera.z - lookAt.z; camera.rotationY = Math.atan2(dz, dx) * (180 / Math.PI) + 270; so no matter the x or z position, the point is always on the mid of the screen, IF and only if y matches with the camera. So what I need is to calculate the rotationX (which are measured in degrees not radians), and I was wondering how I would do this?

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  • Circular Bullet Spread not Even

    - by SoulBeaver
    I'm creating a bullet shooter much in the style of Touhou. Right now I want to have a very simple circular shot being fired from the enemy. See this picture: As you can see, the spacing is very uneven, which isn't very good if you want to survive. The code I'm using is this: private function shoot() : void { const BULLETS_PER_WAVE : int = 72; var interval : Number = BULLETS_PER_WAVE / 360; for (var i : int = 0; i < BULLETS_PER_WAVE; ++i { var xSpeed : Number = GameConstants.BULLET_NORMAL_SPEED_X * Math.sin(i * interval); var ySpeed : Number = GameConstants.BULLET_NORMAL_SPEED_Y * Math.cos(i * interval); BulletFactory.createNormalBullet(bulletColor_, alice_.center, xSpeed, ySpeed); } canShoot_ = false; cooldownTimer_.start(); } I imagine my mistake is in the sin, cos functions, but I'm not entirely sure what's wrong.

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  • Math with Timestamp

    - by Knut Vatsendvik
    table.sql { border-width: 1px; border-spacing: 2px; border-style: dashed; border-color: #0023ff; border-collapse: separate; background-color: white; } table.sql th { border-width: 1px; padding: 1px; border-style: none; border-color: gray; background-color: white; -moz-border-radius: 0px 0px 0px 0px; } table.sql td { border-width: 1px; padding: 3px; border-style: none; border-color: gray; background-color: white; -moz-border-radius: 0px 0px 0px 0px; } .sql-keyword { color: #0000cd; background-color: inherit; } .sql-result { color: #458b74; background-color: inherit; } Got this little SQL quiz from a colleague.  How to add or subtract exactly 1 second from a Timestamp?  Sounded simple enough at first blink, but was a bit trickier than expected. If the data type had been a Date, we knew that we could add or subtract days, minutes or seconds using + or – sysdate + 1 to add one day sysdate - (1 / 24) to subtract one hour sysdate + (1 / 86400) to add one second Would the same arithmetic work with Timestamp as with Date? Let’s test it out with the following query SELECT   systimestamp , systimestamp + (1 / 86400) FROM dual; ---------- 03.05.2010 22.11.50,240887 +02:00 03.05.2010 The first result line shows us the system time down to fractions of seconds. The second result line shows the result as Date (as used for date calculation) meaning now that the granularity is reduced down to a second.   By using the PL/SQL dump() function, we can confirm this with the following query SELECT   dump(systimestamp) , dump(systimestamp + (1 / 86400)) FROM dual; ---------- Typ=188 Len=20: 218,7,5,4,8,53,9,0,200,46,89,20,2,0,5,0,0,0,0,0 Typ=13 Len=8: 218,7,5,4,10,53,10,0 Where typ=13 is a runtime representation for Date. So how can we increase the precision to include fractions of second? After investigating it a bit, we found out that the interval data type INTERVAL DAY TO SECOND could be used with the result of addition or subtraction being a Timestamp. Let’s try again our first query again, now using the interval data type. SELECT systimestamp,    systimestamp + INTERVAL '0 00:00:01.0' DAY TO SECOND(1) FROM dual; ---------- 03.05.2010 22.58.32,723659000 +02:00 03.05.2010 22.58.33,723659000 +02:00 Yes, it worked! To finish the story, here is one example showing how to specify an interval of 2 days, 6 hours, 30 minutes, 4 seconds and 111 thousands of a second. INTERVAL ‘2 6:30:4.111’ DAY TO SECOND(3)

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  • Time passage arithmetic explanation

    - by Cyber Axe
    I ported this from http://www.effectgames.com/effect/article.psp.html/joe/Old_School_Color_Cycling_with_HTML5 some time ago. However i'm now wanting to modify it for the purpose of changing it from floating point to fixed point maths for enhanced efficiency (for those who are going to talk about premature optimization and what not, i want to have my entire engine in fixed point both as a learning process for me and so i can port code more easily to systems in the future that dont have native floating points such as arm cpus) My initial conversion to fixed points just resulted in the cycling stuck on either the first or last frame of cycling. Plus it would be nice to understand better how it works so i can add more options and so forth in the future, my maths however sucks and the comments are limited so i don't really know how the maths work for determining the frame it shoud use (cycleAmount) I was also a beginner when i ported it as i had no idea between floating points and integers and what not. So in summary my question is, can anyone give an explination of the arithmatic used for determining the cycleAmount (which determings the "frame" of the cycle) This is the working floating point maths version of the code: public final void cycle(Colour[] sourceColours, double timeNow, double speedAdjust) { // Cycle all animated colour ranges in palette based on timestamp. sourceColours = sourceColours.clone(); int cycleSize; double cycleRate; double cycleAmount; Cycle cycle; for (int i = 0, len = cycles.length; i < len; ++i) { cycle = cycles[i]; cycleSize = (cycle.HIGH - cycle.LOW) + 1; cycleRate = cycle.RATE / (int) (CYCLE_SPEED / speedAdjust); cycleAmount = 0; if (cycle.REVERSE < 3) { // Standard Cycle cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize); if (cycle.REVERSE < 1) { cycleAmount = cycleSize - cycleAmount; // If below 1 make sure its not reversed. } } else if (cycle.REVERSE == 3) { // Ping-Pong cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize << 1); if (cycleAmount >= cycleSize) { cycleAmount = (cycleSize * 2) - cycleAmount; } } else if (cycle.REVERSE < 6) { // Sine Wave cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize); cycleAmount = Math.sin((cycleAmount * 3.1415926 * 2) / cycleSize) + 1; if (cycle.REVERSE == 4) { cycleAmount *= (cycleSize / 4); } else if (cycle.REVERSE == 5) { cycleAmount *= (cycleSize >> 1); } } if (cycle.REVERSE == 2) { reverseColours(sourceColours, cycle); } if (USE_BLEND_SHIFT) { blendShiftColours(sourceColours, cycle, cycleAmount); } else { shiftColours(sourceColours, cycle, cycleAmount); } if (cycle.REVERSE == 2) { reverseColours(sourceColours, cycle); } } colours = sourceColours; } // This utility function allows for variable precision floating point modulus. private double DFLOAT_MOD(final double d, final double b) { return (Math.floor(d * PRECISION) % Math.floor(b * PRECISION)) / PRECISION; }

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  • LibreOffice Math problem with greek letters

    - by Matheus de Araújo
    I've a problem with my LibreOffice. Using an old archive that I have (with the Maxwell's equations), the greek letters are like squares. I tried to change something in the alphabet but even the font don't have any greek letters (they appear like squares too), both Greek and iGreek letters package. Sounds like a packet that isn't installed or corrupted, but I still redownloaded and reinstalled the LO and I don't know whose I have to install. With the OO my equations worked well (I made the file with it). What am I supposed to do?

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  • Circle collision detection and Vector math: HELP?

    - by Griffin
    Hey so i'm currently going through the wildbunny blog to learn about collision detection, but i'm a bit confused on how the vectors he's talking about come into play QUOTED BLOG: p = ||A-B|| – (r1+r2) The two spheres are penetrating by distance p. We would also like the penetration vector so that we can correct the penetration once we discover it. This is the vector that moves both circles to the point where they just touch, correcting the penetration. Importantly it is not only just a vector that does this, it is the only vector which corrects the penetration by moving the minimum amount. This is important because we only want to correct the error, not introduce more by moving too much when we correct, or too little. N = (A-B) / ||A-B|| P = N*p Here we have calculated the normalised vector N between the two centres and the penetration vector P by multiplying our unit direction by the penetration distance. Ok so i understand that p is the distance each circle is penetrating each other, but i don't get what exactly N and P is. it seems to me N is just the coordinates of the 3rd point of the right trianlge formed by point A and B (A-B) then being divided by the hypotenuse of that triangle or distance between A and B (||A-B||) Whats the significance of this? Also, what is the penetration vector used for? It seems to me like a movement that one of the circles would perform to get un-penetrated.

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  • how to transform child elements position into a world position

    - by MrGreg
    So Im making a 2d space game and I have a bunch of spaceships that have turrets. Objects have a position and orientation, the ships being in world coordinates while the turrets are children and coordinates are relative to their parents. How do I efficiently calculate the position of a turret in world coordinates (i.e. when it fires and I need to know where to place a bullet in the world)? Calculating the turrets orientation is trivial - I just add the turrets relative angle to its parents. For position though, I guess I could do a bunch of trigonometry but this MUST be a common problem with a good/fast general solution? Should I be relearning how to do matrix math again? :) btw - Im creating the game in javascript+canvas but its the math/algorithm im interested in here Cheers, Greg

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  • How to derive euler angles from matrix or quaternion?

    - by KlashnikovKid
    Currently working on steering behavior for my AI and just hit a little mathematical bump. I'm in the process of writing an align function, which basically tries to match the agent's orientation with a target orientation. I've got a good source material for implementing this behavior but it uses euler angles to calculate the rotational delta, acceleration, and so on. This is nice, however I store orientation as a quaternion and the math library I'm using doesn't provide any functionality for deriving the euler angles. But if it helps I also have rotational matrices at my disposal too. What would be the best way to decompose the quaternion or rotational matrix to get the euler information? I found one source for decomposing the matrix, but I'm not quite getting the correct results. I'm thinking it may be a difference of column/row ordering of my matrices but then again, math isn't my strong point. http://nghiaho.com/?page_id=846

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  • 3d trajectory - calculate initial velocity

    - by Skoder
    Hey, I've got a 2D projectile code sample working, but would like to extend it to 3D. How would I calculate the initial velocity of the Z-axis? At the moment, I've got: initVel.X = (float)Math.Cos(45.0); initVel.Y = (float)Math.Sin(45.0); How would I convert this to work in 3D (and add the initial velocity for the Z-axis)? In my example, X is across, Y is up down and Z is going into the screen. I also normalize the vector and multiply it by the speed. Thanks

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  • Building (simple) stellar systems

    - by space borg
    hi I'm currently looking at how to simulate easily some stellar systems (meaning some central stars and then some planets with maybe satellites), in order to allow later some space based strategy game (hence with space ships moving around). This should all be based around time (so the state of each system differs through time) I'm quite struggling with the math behind this topic, like for example: - ellipse related math, - creating the path from planet A to B having time in mind (respective positions will change over time)... Do you know of any resources for that ? I wouldn't mind even buying books about it... thanks in advance best space borg side note: how to display all this stuff isn't a matter at this point in time, I'll simple plans for that (basically sticking to 2D and a "high level view" with no space ships/planets details, just markers)

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