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• Determine arc-length of a Catmull-Rom spline

  - by Wouter

  I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1. Not every spline in this path has the same length. This causes speed differences if I let the weight go at a constant speed for every spline while proceeding along the path. I can remedy this by letting the speed of the weight be dependent on the length of the spline. How can I determine the length of such a spline? Should I just approximate by cutting the spline into 10 straight lines and sum their lengths? I'm using this for dynamic texture mapping on a generated mesh defined by splines.

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• Approximating walking physics via simpler sliding physics

  - by Dave

  I am modeling walking insects. I implement them as cuboids and use forces (including friction and drag), to control motion. However, the movement characteristics of this 'sliding box' physics don't match those due to a legged creature. For example, legged creatures near-instantly accelerate to their top speed; whereas applying a force to a box takes time to accelerate it. The applied force can be increased along with the counteracting drag, giving much quicker acceleration (via force) to a max speed (via drag). However, this also means the force that creatures can exert when pushing on other objects is increased. Does anyone know of any techniques using a physics engine to cheaply model walking creatures?

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• The Numerical ‘Magic’ of Cyclic Numbers

  - by Akemi Iwaya

  If you love crunching numbers or are just a fan of awesome number ‘tricks’ to impress your friends with, then you will definitely want to have a look at cyclic numbers. Dr Tony Padilla from the University of Nottingham shows how these awesome numbers work in Numberphile’s latest video. Cyclic Numbers – Numberphile [YouTube] Want to learn more about cyclic numbers? Then make sure to visit the Wikipedia page linked below! Cyclic number [Wikipedia]     

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• Python — Time complexity of built-in functions versus manually-built functions in finite fields

  - by stackuser

  Generally, I'm wondering about the advantages versus disadvantages of using the built-in arithmetic functions versus rolling your own in Python. Specifically, I'm taking in GF(2) finite field polynomials in string format, converting to base 2 values, performing arithmetic, then output back into polynomials as string format. So a small example of this is in multiplication: Rolling my own: def multiply(a,b): bitsa = reversed("{0:b}".format(a)) g = [(b<<i)*int(bit) for i,bit in enumerate(bitsa)] return reduce(lambda x,y: x+y,g) Versus the built-in: def multiply(a,b): # a,b are GF(2) polynomials in binary form .... return a*b #returns product of 2 polynomials in gf2 Currently, operations like multiplicative inverse (with for example 20 bit exponents) take a long time to run in my program as it's using all of Python's built-in mathematical operations like // floor division and % modulus, etc. as opposed to making my own division, remainder, etc. I'm wondering how much of a gain in efficiency and performance I can get by building these manually (as shown above). I realize the gains are dependent on how well the manual versions are built, that's not the question. I'd like to find out 'basically' how much advantage there is over the built-in's. So for instance, if multiplication (as in the example above) is well-suited for base 10 (decimal) arithmetic but has to jump through more hoops to change bases to binary and then even more hoops in operating (so it's lower efficiency), that's what I'm wondering. Like, I'm wondering if it's possible to bring the time down significantly by building them myself in ways that maybe some professionals here have already come across.

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• How could you parallelise a 2D boids simulation

  - by Sycren

  How could you program a 2D boids simulation in such a way that it could use processing power from different sources (clusters, gpu). In the above example, the non-coloured particles move around until they cluster (yellow) and stop moving. The problem is that all the entities could potentially interact with each other although an entity in the top left is unlikely to interact with one in the bottom right. If the domain was split into different segments, it may speed the whole thing up, But if an entity wanted to cross into another segment there may be problems. At the moment this simulation works with 5000 entities with a good frame rate, I would like to try this with millions if possible. Would it be possible to use quad trees to further optimise this? Any other suggestions?

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• Follow point of interest by applying torque

  - by azymm

  Given a body with an orientation angle and a point of interest or targetAngle, is there an elegant solution for keeping the body oriented towards the point of interest by applying torque or impulses? I have a naive solution working below, but the effect is pretty 'wobbly', it'll overshoot each time, slowly getting closer to the target angle - undesirable effect in my case. I'd like to find a solution that is more intelligent - that can accelerate to near the target angle then decelerate and stop right at the target angle (or within a small range). If it helps, I'm using box2d and the body is a rectangle. def gameloop(dt): targetAngle = get_target_angle() bodyAngle = get_body_angle() deltaAngle = targetAngle - bodyAngle if deltaAngle > PI: deltaAngle = targetAngle - (bodyAngle + 2.0 * PI) if deltaAngle < -PI: deltaAngle = targetAngle - (bodyAngle - 2.0 * PI) # multiply by 2, for stronger reaction deltaAngle = deltaAngle * 2.0; body.apply_torque(deltaAngle); One other thing, when body has no linear velocity, the above solution works ok. But when the body has some linear velocity, the solution above causes really wonky movement. Not sure why, but would appreciate any hints as to why that might be.

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• I love programming but never get projects started

  - by 0xHenry

  I read this question and the most voted answer and said to myself "Those things are what I want to do! But why the heck I'm not doing it?" The problem here is that I can't get anything started. I hope you get some kind of idea what I'm interested in and can help me continue programming. I'm interested in embedded programming and I'd like to learn some ARM assembly. I think those could be combined with image processing. Also I'd love to create programs that are actually useful to some people but it seems like there are already multiple programs for pretty much every purpose. Maybe if I found an interesting program without open source alternatives I could get a great project to work on. How could I get myself to finally start a project or few and keep myself interested in them? I just want to get myself to do something I love.

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• How Big Is a Billion? [Video]

  - by Jason Fitzpatrick

  A billion is a billion except, when it isn’t. Depending on where and when you were raised and educated, the world “billion” is some magnitudes different–read on to see the difference between a billion in long and short number systems. [via Geeks Are Sexy] Here’s How to Download Windows 8 Release Preview Right Now HTG Explains: Why Linux Doesn’t Need Defragmenting How to Convert News Feeds to Ebooks with Calibre

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• LibGDX Boid Seek Behaviour

  - by childonline

  I'm trying to make a swarm of boids which seek out the mouse position and move towards it, but I'm having a bit of a problem. The boids just seem to want to go to upper-right corner of the game window. The mouse position seems influence the behavior a bit, but not enough to make the boid turn towards it. I suspect there is a problem with the way LibGDX handles its coordinate system, but I'm not sure how to fix it I've uploaded the eclipse project here! Also here are the relevant bits of my code, in case you see something obviously wrong: public Agent(){ _texture = GdxGame.TEX_AGENT; TextureRegion region = new TextureRegion(_texture, 0, 0, 32, 32); TextureRegion region2 = new TextureRegion(GdxGame.TEX_TARGET, 0, 0, 32, 32); _sprite = new Sprite(region); _sprite.setSize(.05f, .05f); _sprite_target = new Sprite(region2); _sprite_target.setSize(.1f, .1f); _max_velocity = 0.05f; _max_speed = 0.005f; _velocity = new Vector2(0, 0); _desired_velocity = new Vector2(0, 0); _steering = new Vector2(0, 0); _position = new Vector2(-_sprite.getWidth()/2, -_sprite.getHeight()/2); _mass = 10f; } public void Update(float deltaTime){ _target = new Vector2(Gdx.input.getX(), Gdx.input.getY()); _desired_velocity = ((_target.sub(_position)).nor()).scl(_max_velocity,_max_velocity); _steering = ((_desired_velocity.sub(_velocity)).limit(_max_speed)).div(_mass); _velocity = (_velocity.add(_steering)).limit(_max_speed); _position = _position.add(_velocity); _sprite.setPosition(_position.x, _position.y); _sprite_target.setPosition(Gdx.input.getX(), Gdx.input.getY()); } I've used this tutorial here. Thanks!

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• Atmospheric Scattering

  - by Lawrence Kok

  I'm trying to implement atmospheric scattering based on Sean O`Neil algorithm that was published in GPU Gems 2. But I have some trouble getting the shader to work. My latest attempts resulted in: http://img253.imageshack.us/g/scattering01.png/ I've downloaded sample code of O`Neil from: http://http.download.nvidia.com/developer/GPU_Gems_2/CD/Index.html. Made minor adjustments to the shader 'SkyFromAtmosphere' that would allow it to run in AMD RenderMonkey. In the images it is see-able a form of banding occurs, getting an blueish tone. However it is only applied to one half of the sphere, the other half is completely black. Also the banding appears to occur at Zenith instead of Horizon, and for a reason I managed to get pac-man shape. I would appreciate it if somebody could show me what I'm doing wrong. Vertex Shader: uniform mat4 matView; uniform vec4 view_position; uniform vec3 v3LightPos; const int nSamples = 3; const float fSamples = 3.0; const vec3 Wavelength = vec3(0.650,0.570,0.475); const vec3 v3InvWavelength = 1.0f / vec3( Wavelength.x * Wavelength.x * Wavelength.x * Wavelength.x, Wavelength.y * Wavelength.y * Wavelength.y * Wavelength.y, Wavelength.z * Wavelength.z * Wavelength.z * Wavelength.z); const float fInnerRadius = 10; const float fOuterRadius = fInnerRadius * 1.025; const float fInnerRadius2 = fInnerRadius * fInnerRadius; const float fOuterRadius2 = fOuterRadius * fOuterRadius; const float fScale = 1.0 / (fOuterRadius - fInnerRadius); const float fScaleDepth = 0.25; const float fScaleOverScaleDepth = fScale / fScaleDepth; const vec3 v3CameraPos = vec3(0.0, fInnerRadius * 1.015, 0.0); const float fCameraHeight = length(v3CameraPos); const float fCameraHeight2 = fCameraHeight * fCameraHeight; const float fm_ESun = 150.0; const float fm_Kr = 0.0025; const float fm_Km = 0.0010; const float fKrESun = fm_Kr * fm_ESun; const float fKmESun = fm_Km * fm_ESun; const float fKr4PI = fm_Kr * 4 * 3.141592653; const float fKm4PI = fm_Km * 4 * 3.141592653; varying vec3 v3Direction; varying vec4 c0, c1; float scale(float fCos) { float x = 1.0 - fCos; return fScaleDepth * exp(-0.00287 + x*(0.459 + x*(3.83 + x*(-6.80 + x*5.25)))); } void main( void ) { // Get the ray from the camera to the vertex, and its length (which is the far point of the ray passing through the atmosphere) vec3 v3FrontColor = vec3(0.0, 0.0, 0.0); vec3 v3Pos = normalize(gl_Vertex.xyz) * fOuterRadius; vec3 v3Ray = v3CameraPos - v3Pos; float fFar = length(v3Ray); v3Ray = normalize(v3Ray); // Calculate the ray's starting position, then calculate its scattering offset vec3 v3Start = v3CameraPos; float fHeight = length(v3Start); float fDepth = exp(fScaleOverScaleDepth * (fInnerRadius - fCameraHeight)); float fStartAngle = dot(v3Ray, v3Start) / fHeight; float fStartOffset = fDepth*scale(fStartAngle); // Initialize the scattering loop variables float fSampleLength = fFar / fSamples; float fScaledLength = fSampleLength * fScale; vec3 v3SampleRay = v3Ray * fSampleLength; vec3 v3SamplePoint = v3Start + v3SampleRay * 0.5; // Now loop through the sample rays for(int i=0; i<nSamples; i++) { float fHeight = length(v3SamplePoint); float fDepth = exp(fScaleOverScaleDepth * (fInnerRadius - fHeight)); float fLightAngle = dot(normalize(v3LightPos), v3SamplePoint) / fHeight; float fCameraAngle = dot(normalize(v3Ray), v3SamplePoint) / fHeight; float fScatter = (-fStartOffset + fDepth*( scale(fLightAngle) - scale(fCameraAngle)))/* 0.25f*/; vec3 v3Attenuate = exp(-fScatter * (v3InvWavelength * fKr4PI + fKm4PI)); v3FrontColor += v3Attenuate * (fDepth * fScaledLength); v3SamplePoint += v3SampleRay; } // Finally, scale the Mie and Rayleigh colors and set up the varying variables for the pixel shader vec4 newPos = vec4( (gl_Vertex.xyz + view_position.xyz), 1.0); gl_Position = gl_ModelViewProjectionMatrix * vec4(newPos.xyz, 1.0); gl_Position.z = gl_Position.w * 0.99999; c1 = vec4(v3FrontColor * fKmESun, 1.0); c0 = vec4(v3FrontColor * (v3InvWavelength * fKrESun), 1.0); v3Direction = v3CameraPos - v3Pos; } Fragment Shader: uniform vec3 v3LightPos; varying vec3 v3Direction; varying vec4 c0; varying vec4 c1; const float g =-0.90f; const float g2 = g * g; const float Exposure =2; void main(void){ float fCos = dot(normalize(v3LightPos), v3Direction) / length(v3Direction); float fMiePhase = 1.5 * ((1.0 - g2) / (2.0 + g2)) * (1.0 + fCos*fCos) / pow(1.0 + g2 - 2.0*g*fCos, 1.5); gl_FragColor = c0 + fMiePhase * c1; gl_FragColor.a = 1.0; }

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• Mathematics for Computer Science

  - by jiewmeng

  I am going into university next year. I think maths would be one of the more important aspects of computer science? I recently saw the MIT Intro to Algorithms video on YouTube and the maths required is quite hardcore. I wonder what parts of maths do i need, probability, calculus, trigo etc. Will the book Concrete Mathematics - it claims to be foundation for computer science - on Amazon cover most of whats required?

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• How to develop RPG Damage Formulas?

  - by user127817

  I'm developing a classical 2d RPG (in a similar vein to final fantasy) and I was wondering if anyone had some advice on how to do damage formulas/links to resources/examples? I'll explain my current setup. Hopefully I'm not overdoing it with this question, and I apologize if my questions is too large/broad My Characters stats are composed of the following: enum Stat { HP = 0, MP = 1, SP = 2, Strength = 3, Vitality = 4, Magic = 5, Spirit = 6, Skill = 7, Speed = 8, //Speed/Agility are the same thing Agility = 8, Evasion = 9, MgEvasion = 10, Accuracy = 11, Luck = 12, }; Vitality is basically defense to physical attacks and spirit is defense to magic attacks. All stats have fixed maximums (9999 for HP, 999 for MP/SP and 255 for the rest). With abilities, the maximums can be increased (99999 for HP, 9999 for HP/SP, 999 for the rest) with typical values (at level 100) before/after abilities+equipment+etc will be 8000/20,000 for HP, 800/2000 for SP/MP, 180/350 for other stats Late game Enemy HP will typically be in the lower millions (with a super boss having the maximum of ~12 million). I was wondering how do people actually develop proper damage formulas that scale correctly? For instance, based on this data, using the damage formulas for Final Fantasy X as a base looked very promising. A full reference here http://www.gamefaqs.com/ps2/197344-final-fantasy-x/faqs/31381 but as a quick example: Str = 127, 'Attack' command used, enemy Def = 34. 1. Physical Damage Calculation: Step 1 ------------------------------------- [{(Stat^3 ÷ 32) + 32} x DmCon ÷16] Step 2 ---------------------------------------- [{(127^3 ÷ 32) + 32} x 16 ÷ 16] Step 3 -------------------------------------- [{(2048383 ÷ 32) + 32} x 16 ÷ 16] Step 4 --------------------------------------------------- [{(64011) + 32} x 1] Step 5 -------------------------------------------------------- [{(64043 x 1)}] Step 6 ---------------------------------------------------- Base Damage = 64043 Step 7 ----------------------------------------- [{(Def - 280.4)^2} ÷ 110] + 16 Step 8 ------------------------------------------ [{(34 - 280.4)^2} ÷ 110] + 16 Step 9 ------------------------------------------------- [(-246)^2) ÷ 110] + 16 Step 10 ---------------------------------------------------- [60516 ÷ 110] + 16 Step 11 ------------------------------------------------------------ [550] + 16 Step 12 ---------------------------------------------------------- DefNum = 566 Step 13 ---------------------------------------------- [BaseDmg * DefNum ÷ 730] Step 14 --------------------------------------------------- [64043 * 566 ÷ 730] Step 15 ------------------------------------------------------ [36248338 ÷ 730] Step 16 ------------------------------------------------- Base Damage 2 = 49655 Step 17 ------------ Base Damage 2 * {730 - (Def * 51 - Def^2 ÷ 11) ÷ 10} ÷ 730 Step 18 ---------------------- 49655 * {730 - (34 * 51 - 34^2 ÷ 11) ÷ 10} ÷ 730 Step 19 ------------------------- 49655 * {730 - (1734 - 1156 ÷ 11) ÷ 10} ÷ 730 Step 20 ------------------------------- 49655 * {730 - (1734 - 105) ÷ 10} ÷ 730 Step 21 ------------------------------------- 49655 * {730 - (1629) ÷ 10} ÷ 730 Step 22 --------------------------------------------- 49655 * {730 - 162} ÷ 730 Step 23 ----------------------------------------------------- 49655 * 568 ÷ 730 Step 24 -------------------------------------------------- Final Damage = 38635 I simply modified the dividers to include the attack rating of weapons and the armor rating of armor. Magic Damage is calculated as follows: Mag = 255, Ultima is used, enemy MDef = 1 Step 1 ----------------------------------- [DmCon * ([Stat^2 ÷ 6] + DmCon) ÷ 4] Step 2 ------------------------------------------ [70 * ([255^2 ÷ 6] + 70) ÷ 4] Step 3 ------------------------------------------ [70 * ([65025 ÷ 6] + 70) ÷ 4] Step 4 ------------------------------------------------ [70 * (10837 + 70) ÷ 4] Step 5 ----------------------------------------------------- [70 * (10907) ÷ 4] Step 6 ------------------------------------ Base Damage = 190872 [cut to 99999] Step 7 ---------------------------------------- [{(MDef - 280.4)^2} ÷ 110] + 16 Step 8 ------------------------------------------- [{(1 - 280.4)^2} ÷ 110] + 16 Step 9 ---------------------------------------------- [{(-279.4)^2} ÷ 110] + 16 Step 10 -------------------------------------------------- [(78064) ÷ 110] + 16 Step 11 ------------------------------------------------------------ [709] + 16 Step 12 --------------------------------------------------------- MDefNum = 725 Step 13 --------------------------------------------- [BaseDmg * MDefNum ÷ 730] Step 14 --------------------------------------------------- [99999 * 725 ÷ 730] Step 15 ------------------------------------------------- Base Damage 2 = 99314 Step 16 ---------- Base Damage 2 * {730 - (MDef * 51 - MDef^2 ÷ 11) ÷ 10} ÷ 730 Step 17 ------------------------ 99314 * {730 - (1 * 51 - 1^2 ÷ 11) ÷ 10} ÷ 730 Step 18 ------------------------------ 99314 * {730 - (51 - 1 ÷ 11) ÷ 10} ÷ 730 Step 19 --------------------------------------- 99314 * {730 - (49) ÷ 10} ÷ 730 Step 20 ----------------------------------------------------- 99314 * 725 ÷ 730 Step 21 -------------------------------------------------- Final Damage = 98633 The problem is that the formulas completely fall apart once stats start going above 255. In particular Defense values over 300 or so start generating really strange behavior. High Strength + Defense stats lead to massive negative values for instance. While I might be able to modify the formulas to work correctly for my use case, it'd probably be easier just to use a completely new formula. How do people actually develop damage formulas? I was considering opening excel and trying to build the formula that way (mapping Attack Stats vs. Defense Stats for instance) but I was wondering if there's an easier way? While I can't convey the full game mechanics of my game here, might someone be able to suggest a good starting place for building a damage formula? Thanks

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• Billboarding + aligning with velocity direction

  - by roxlu

  I'm working on a particle system where I'm orientating the billboard using the inverted orientation matrix of my camera. This works quite well and my quad are rotated correctly towards the camera. But, now I want to to rotate the quads in such a way that they point towards the direction they are going to. In 2D this can be done by normalizing the velocity vector and using that vector for a rotation around the Z-axis (where vel.x = cos(a) and vel.y = sin(a)). But how does this work in 3D? Thanks roxlu

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• Is it possible to billboard a sprite using a transformation matrix?

  - by Ross

  None of the current topics on billboarding seemed to answer this question. But, given a sprite (or quad) that has it's own 4x4 transformation matrix a camera with a view matrix (a standard 4x4 transformation matrix) is it possible to compute a 4x4 transformation matrix such that when the quad's matrix is multiplied with this matrix it has an orientation of looking at the camera? Thank you in advance.

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• How to create projection/view matrix for hole in the monitor effect

  - by Mr Bell

  Lets say I have my XNA app window that is sized at 640 x 480 pixels. Now lets say I have a cube model with its poly's facing in to make a room. This cube is sized 640 units wide by 480 units high by 480 units deep. Lets say the camera is somewhere in front of the box looking at it. How can I set up the view and projection matrices such that the front edge of the box lines up exactly with the edges of the application window? It seems like this should probably involve the Matrix.CreatePerspectiveOffCenter method, but I don't fully understand how the parameters translate on to the screen. For reference, the end result will be something like Johhny Lee's wii head tracking demo: http://www.youtube.com/watch?v=Jd3-eiid-Uw&feature=player_embedded P.S. I realize that his source code is available, but I am afraid I haven't been able to make heads or tails out of it.

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• Converting from different handedness coordinate systems

  - by SirYakalot

  I am currently porting a demo from XNA to DirectX which, as I understand it, both have coordinate systems with different handednesses. What are the things I need to bare in mind when converting between the two? I understand not everything needs to be changed. Also I notice that many of the 3D maths functions in some of the direct3D libraries have right handed and left handed alternatives. Would it be better to just use these?

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• Surface of Revolution with 3D surface

  - by user5584

  I have to use this function to get a Surface of Revolution (homework). newVertex = (oldVertex.y, someFunc1(oldVertex.x, oldVertex.y), someFunc2(oldVertex.x, oldVertex.y)); As far as I know (FIXME) Surface of Revolution means rotations of a (2D)curve around an axis in 3D. But this vertex computing gives a 3D plane (FIXME again :D), so rotation of this isn't obvious. Am I misunderstanding something?

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• Derive a algorithm to match best position

  - by Farooq Arshed

  I have pieces in my game which have stats and cost assigned to them and they can only be placed at a certain location. Lets say I have 50 pieces. e.g. Piece1 = 100 stats, 10 cost, Position A. Piece2 = 120 stats, 5 cost, Position B. Piece3 = 500 stats, 50 cost, Position C. Piece4 = 200 stats, 25 cost, Position A. and so on.. I have a board on which 12 pieces have to be allocated and have to remain inside the board cost. e.g. A board has A,B,C ... J,K,L positions and X Cost assigned to it. I have to figure out a way to place best possible piece in the correct position and should remain within the cost specified by the board. Any help would be appreciated.

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• How to develop RPG Damage Formulas?

  - by user127817

  I'm developing a classical 2d RPG (in a similar vein to final fantasy) and I was wondering if anyone had some advice on how to do damage formulas/links to resources/examples? I'll explain my current setup. Hopefully I'm not overdoing it with this question, and I apologize if my questions is too large/broad My Characters stats are composed of the following: enum Stat { HP = 0, MP = 1, SP = 2, Strength = 3, Vitality = 4, Magic = 5, Spirit = 6, Skill = 7, Speed = 8, //Speed/Agility are the same thing Agility = 8, Evasion = 9, MgEvasion = 10, Accuracy = 11, Luck = 12, }; Vitality is basically defense to physical attacks and spirit is defense to magic attacks. All stats have fixed maximums (9999 for HP, 999 for MP/SP and 255 for the rest). With abilities, the maximums can be increased (99999 for HP, 9999 for HP/SP, 999 for the rest) with typical values (at level 100) before/after abilities+equipment+etc will be 8000/20,000 for HP, 800/2000 for SP/MP, 180/350 for other stats Late game Enemy HP will typically be in the lower millions (with a super boss having the maximum of ~12 million). I was wondering how do people actually develop proper damage formulas that scale correctly? For instance, based on this data, using the damage formulas for Final Fantasy X as a base looked very promising. A full reference here http://www.gamefaqs.com/ps2/197344-final-fantasy-x/faqs/31381 but as a quick example: Str = 127, 'Attack' command used, enemy Def = 34. 1. Physical Damage Calculation: Step 1 ------------------------------------- [{(Stat^3 ÷ 32) + 32} x DmCon ÷16] Step 2 ---------------------------------------- [{(127^3 ÷ 32) + 32} x 16 ÷ 16] Step 3 -------------------------------------- [{(2048383 ÷ 32) + 32} x 16 ÷ 16] Step 4 --------------------------------------------------- [{(64011) + 32} x 1] Step 5 -------------------------------------------------------- [{(64043 x 1)}] Step 6 ---------------------------------------------------- Base Damage = 64043 Step 7 ----------------------------------------- [{(Def - 280.4)^2} ÷ 110] + 16 Step 8 ------------------------------------------ [{(34 - 280.4)^2} ÷ 110] + 16 Step 9 ------------------------------------------------- [(-246)^2) ÷ 110] + 16 Step 10 ---------------------------------------------------- [60516 ÷ 110] + 16 Step 11 ------------------------------------------------------------ [550] + 16 Step 12 ---------------------------------------------------------- DefNum = 566 Step 13 ---------------------------------------------- [BaseDmg * DefNum ÷ 730] Step 14 --------------------------------------------------- [64043 * 566 ÷ 730] Step 15 ------------------------------------------------------ [36248338 ÷ 730] Step 16 ------------------------------------------------- Base Damage 2 = 49655 Step 17 ------------ Base Damage 2 * {730 - (Def * 51 - Def^2 ÷ 11) ÷ 10} ÷ 730 Step 18 ---------------------- 49655 * {730 - (34 * 51 - 34^2 ÷ 11) ÷ 10} ÷ 730 Step 19 ------------------------- 49655 * {730 - (1734 - 1156 ÷ 11) ÷ 10} ÷ 730 Step 20 ------------------------------- 49655 * {730 - (1734 - 105) ÷ 10} ÷ 730 Step 21 ------------------------------------- 49655 * {730 - (1629) ÷ 10} ÷ 730 Step 22 --------------------------------------------- 49655 * {730 - 162} ÷ 730 Step 23 ----------------------------------------------------- 49655 * 568 ÷ 730 Step 24 -------------------------------------------------- Final Damage = 38635 I simply modified the dividers to include the attack rating of weapons and the armor rating of armor. Magic Damage is calculated as follows: Mag = 255, Ultima is used, enemy MDef = 1 Step 1 ----------------------------------- [DmCon * ([Stat^2 ÷ 6] + DmCon) ÷ 4] Step 2 ------------------------------------------ [70 * ([255^2 ÷ 6] + 70) ÷ 4] Step 3 ------------------------------------------ [70 * ([65025 ÷ 6] + 70) ÷ 4] Step 4 ------------------------------------------------ [70 * (10837 + 70) ÷ 4] Step 5 ----------------------------------------------------- [70 * (10907) ÷ 4] Step 6 ------------------------------------ Base Damage = 190872 [cut to 99999] Step 7 ---------------------------------------- [{(MDef - 280.4)^2} ÷ 110] + 16 Step 8 ------------------------------------------- [{(1 - 280.4)^2} ÷ 110] + 16 Step 9 ---------------------------------------------- [{(-279.4)^2} ÷ 110] + 16 Step 10 -------------------------------------------------- [(78064) ÷ 110] + 16 Step 11 ------------------------------------------------------------ [709] + 16 Step 12 --------------------------------------------------------- MDefNum = 725 Step 13 --------------------------------------------- [BaseDmg * MDefNum ÷ 730] Step 14 --------------------------------------------------- [99999 * 725 ÷ 730] Step 15 ------------------------------------------------- Base Damage 2 = 99314 Step 16 ---------- Base Damage 2 * {730 - (MDef * 51 - MDef^2 ÷ 11) ÷ 10} ÷ 730 Step 17 ------------------------ 99314 * {730 - (1 * 51 - 1^2 ÷ 11) ÷ 10} ÷ 730 Step 18 ------------------------------ 99314 * {730 - (51 - 1 ÷ 11) ÷ 10} ÷ 730 Step 19 --------------------------------------- 99314 * {730 - (49) ÷ 10} ÷ 730 Step 20 ----------------------------------------------------- 99314 * 725 ÷ 730 Step 21 -------------------------------------------------- Final Damage = 98633 The problem is that the formulas completely fall apart once stats start going above 255. In particular Defense values over 300 or so start generating really strange behavior. High Strength + Defense stats lead to massive negative values for instance. While I might be able to modify the formulas to work correctly for my use case, it'd probably be easier just to use a completely new formula. How do people actually develop damage formulas? I was considering opening excel and trying to build the formula that way (mapping Attack Stats vs. Defense Stats for instance) but I was wondering if there's an easier way? While I can't convey the full game mechanics of my game here, might someone be able to suggest a good starting place for building a damage formula? Thanks

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• Why doesn't Unity's OnCollisionEnter give me surface normals, and what's the most reliable way to get them?

  - by michael.bartnett

  Unity's on collision event gives you a Collision object that gives you some information about the collision that happened (including a list of ContactPoints with hit normals). But what you don't get is surface normals for the collider that you hit. Here's a screenshot to illustrate. The red line is from ContactPoint.normal and the blue line is from RaycastHit.normal. Is this an instance of Unity hiding information to provide a simplified API? Or do standard 3D realtime collision detection techniques just not collect this information? And for the second part of the question, what's a surefire and relatively efficient way to get a surface normal for a collision? I know that raycasting gives you surface normals, but it seems I need to do several raycasts to accomplish this for all scenarios (maybe a contact point/normal combination misses the collider on the first cast, or maybe you need to do some average of all the contact points' normals to get the best result). My current method: Back up the Collision.contacts[0].point along its hit normal Raycast down the negated hit normal for float.MaxValue, on Collision.collider If that fails, repeat steps 1 and 2 with the non-negated normal If that fails, try steps 1 to 3 with Collision.contacts[1] Repeat 4 until successful or until all contact points exhausted. Give up, return Vector3.zero. This seems to catch everything, but all those raycasts make me queasy, and I'm not sure how to test that this works for enough cases. Is there a better way?

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• Blending animations for more character movements

  - by Noob Saibot

  I am making a hack n slash 3rd person game. And I want the character movements to be more dynamic not like fighting games where you have a moves list. I want to animate tons of different animations and have them "Tween" between each other? Because I want the controls to not be keyboard mouse. I want it to be all keyboard. that way you have up to 10 inputs (All your fingers) to blend and morph animations to create more fluid movements. In the end this will almost be similar to characters typing a phrase or string of keys rather than move forward mouse look click to melee. My question is. Has anyone done this before and would someone go about trying to tween lets say one for key on the keyboard excluding Tab, Caps, R+Shift, L+Shift, Enter, R+Ctrl, L+Ctrl, L+Alt, R+Alt, Windows Key, and Menu. So thats all the numbers, letters and punctuation keys. Thats 46 keys gives me a combination of 46P1 = 5502622159812088949850305428800254892961651752960000000000L (used Python) and with a minimum entry value of 2 keypresses shortening to half. This is not humanly possible to create so many inique animations in one lifetime. But I'm guessing there is a reason this hasn't been done already. Or if I just used 10 basic keys. Maybe ASDF SPACE (RIGHT HAND) 456+0 (LEFT HAND KEYPAD) it would give me 3,628,800 posible unique animations.

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• Project collision shapes to plane for 2.5D collision detection

  - by Jkh2

  I am working on a top down 2.5D game. In the game anything that overlaps on the screen should be 'colliding' with each other regardless of whether they are on the same plane in the 3D world. This is illustrated below from a side-ways view: The orange and green circles are spheres floating in the 3D world. They are projected onto a plane parallel to the viewport plane (y = 0 in the image) and if they overlap there is a collision event between them. These spheres are attached to other meshes to represent the sphere bounding boxes for collisions. The way I plan to implement this at the moment is the following: Get the 3D world position at the center of the sphere. Use Camera.WorldToViewportPoint to project the point to the viewport plane. Move a Sphere Collider with the radius of the sphere to that point. Test for collisions using unity colliders. My question is how to extend this to work for rotated cuboids. For instance if I have two rotated cuboids, if I follow the logic above it would not work as intended as the cuboids may not collide but they could still be intersected on the view plane. An example is below: Is there a way to project a cuboid that would be aligned with the plane? Would it be a valid cuboid for all rotations if I did this?

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• Transform 3D vectors between coordinate systems

  - by Nir Cig

  I've got 6 points in 3D space: A,B,C,D,E,F, that represent 4 vectors. AB is perpendicular to AC and DE is perpendicular to DF. I need to find a transformation matrix M, that transforms AB to DE and AC to DF. In other words: M·AB=DE, M·AC=DF If no scaling was involved, this could be solved with a simple rotation matrix. But since the ratios |AB|/|DE|, |AC|/|DF| might be different, I'm not sure how to proceed.

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• Camera lookAt target changes when rotating parent node

  - by Michael IV

  have the following issue.I have a camera with lookAt method which works fine.I have a parent node to which I parent the camera.If I rotate the parent node while keeping the camera lookAt the target , the camera lookAt changes too.That is nor what I want to achieve.I need it to work like in Adobe AE when you parent camera to a null object:when null object is rotated the camera starts orbiting around the target while still looking at the target.What I do currently is multiplying parent's model matrix with camera model matrix which is calculated from lookAt() method.I am sure I need to decompose (or recompose ) one of the matrices before multiplying them .Parent model or camera model ? Anyone here can show the right way doing it ? UPDATE: The parent is just a node .The child is the camera.The parented camera in AfterEffects works like this: If you rotate the parent node while camera looks at the target , the camera actually starts orbiting around the target based on the parent rotation.In my case the parent rotation changes also Camera's lookAt direction which IS NOT what I want.Hope now it is clear .

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• Rotate/Translate object in local space

  - by Mathias Hölzl

  I am just trying to create a movementcontroller class for game entities. These class should transform the entity affected by the mouse and keyboard input. I am able to calculate the changed rotation and the new globalPosition. Then I multiply: newGlobalMatrix = changedRotationMatrix * oldGlobalMatrix; newGlobalMatrix = MatrixSetPosition(newPosition); The problem is that the object rotates around the global axis and not around the local axis. I use XNAMath for the matrix calculation.

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