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  • Matlab help: I am given a second order differential equation.I need to use matlab to find unit step response and impulse response?

    - by Cady Smith
    I have the second order differential equation d^2(y(t))/dt^2+ B1*d(y(t))/dt+ c1*y(t)=A1*x(t) t is in seconds and is greater than 0. A1, B1, C1 are constants that equal: A1= 3.8469x10^6 B1= 325.6907 C1= 3.8469x10^6 This system is linear, time-invariant, and casual. The system is called H1. I want to use Matlab to compute and plot the impulse response function h1(t) and the unit step response function g1(t) of this system.

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  • Logic error for Gauss elimination

    - by iwanttoprogram
    Logic error problem with the Gaussian Elimination code...This code was from my Numerical Methods text in 1990's. The code is typed in from the book- not producing correct output... Sample Run: SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS USING GAUSSIAN ELIMINATION This program uses Gaussian Elimination to solve the system Ax = B, where A is the matrix of known coefficients, B is the vector of known constants and x is the column matrix of the unknowns. Number of equations: 3 Enter elements of matrix [A] A(1,1) = 0 A(1,2) = -6 A(1,3) = 9 A(2,1) = 7 A(2,2) = 0 A(2,3) = -5 A(3,1) = 5 A(3,2) = -8 A(3,3) = 6 Enter elements of [b] vector B(1) = -3 B(2) = 3 B(3) = -4 SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS The solution is x(1) = 0.000000 x(2) = -1.#IND00 x(3) = -1.#IND00 Determinant = -1.#IND00 Press any key to continue . . . The code as copied from the text... //Modified Code from C Numerical Methods Text- June 2009 #include <stdio.h> #include <math.h> #define MAXSIZE 20 //function prototype int gauss (double a[][MAXSIZE], double b[], int n, double *det); int main(void) { double a[MAXSIZE][MAXSIZE], b[MAXSIZE], det; int i, j, n, retval; printf("\n \t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS"); printf("\n \t USING GAUSSIAN ELIMINATION \n"); printf("\n This program uses Gaussian Elimination to solve the"); printf("\n system Ax = B, where A is the matrix of known"); printf("\n coefficients, B is the vector of known constants"); printf("\n and x is the column matrix of the unknowns."); //get number of equations n = 0; while(n <= 0 || n > MAXSIZE) { printf("\n Number of equations: "); scanf ("%d", &n); } //read matrix A printf("\n Enter elements of matrix [A]\n"); for (i = 0; i < n; i++) for (j = 0; j < n; j++) { printf(" A(%d,%d) = ", i + 1, j + 1); scanf("%lf", &a[i][j]); } //read {B} vector printf("\n Enter elements of [b] vector\n"); for (i = 0; i < n; i++) { printf(" B(%d) = ", i + 1); scanf("%lf", &b[i]); } //call Gauss elimination function retval = gauss(a, b, n, &det); //print results if (retval == 0) { printf("\n\t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS\n"); printf("\n\t The solution is"); for (i = 0; i < n; i++) printf("\n \t x(%d) = %lf", i + 1, b[i]); printf("\n \t Determinant = %lf \n", det); } else printf("\n \t SINGULAR MATRIX \n"); return 0; } /* Solves the system of equations [A]{x} = {B} using */ /* the Gaussian elimination method with partial pivoting. */ /* Parameters: */ /* n - number of equations */ /* a[n][n] - coefficient matrix */ /* b[n] - right-hand side vector */ /* *det - determinant of [A] */ int gauss (double a[][MAXSIZE], double b[], int n, double *det) { double tol, temp, mult; int npivot, i, j, l, k, flag; //initialization *det = 1.0; tol = 1e-30; //initial tolerance value npivot = 0; //mult = 0; //forward elimination for (k = 0; k < n; k++) { //search for max coefficient in pivot row- a[k][k] pivot element for (i = k + 1; i < n; i++) { if (fabs(a[i][k]) > fabs(a[k][k])) { //interchange row with maxium element with pivot row npivot++; for (l = 0; l < n; l++) { temp = a[i][l]; a[i][l] = a[k][l]; a[k][l] = temp; } temp = b[i]; b[i] = b[k]; b[k] = temp; } } //test for singularity if (fabs(a[k][k]) < tol) { //matrix is singular- terminate flag = 1; return flag; } //compute determinant- the product of the pivot elements *det = *det * a[k][k]; //eliminate the coefficients of X(I) for (i = k; i < n; i++) { mult = a[i][k] / a[k][k]; b[i] = b[i] - b[k] * mult; //compute constants for (j = k; j < n; j++) //compute coefficients a[i][j] = a[i][j] - a[k][j] * mult; } } //adjust the sign of the determinant if(npivot % 2 == 1) *det = *det * (-1.0); //backsubstitution b[n] = b[n] / a[n][n]; for(i = n - 1; i > 1; i--) { for(j = n; j > i + 1; j--) b[i] = b[i] - a[i][j] * b[j]; b[i] = b[i] / a[i - 1][i]; } flag = 0; return flag; } The solution should be: 1.058824, 1.823529, 0.882353 with det as -102.000000 Any insight is appreciated...

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  • error in encryption program

    - by Raja
    #include<iostream> #include<math.h> #include<string> using namespace std; int gcd(int n,int m) { if(m<=n && n%m ==0) return m; if(n<m) return gcd(m,n); else return gcd(m,n%m); } int REncryptText(char m) { int p = 11, q = 3; int e = 3; int n = p * q; int phi = (p - 1) * (q - 1); int check1 = gcd(e, p - 1); int check2 = gcd(e, q - 1); int check3 = gcd(e, phi); // // Compute d such that ed = 1 (mod phi) //i.e. compute d = e-1 mod phi = 3-1 mod 20 //i.e. find a value for d such that phi divides (ed-1) //i.e. find d such that 20 divides 3d-1. //Simple testing (d = 1, 2, ...) gives d = 7 // double d = Math.Pow(e, -1) % phi; int d = 7; // public key = (n,e) // (33,3) //private key = (n,d) //(33 ,7) double g = pow(m,e); int ciphertext = g %n; // Now say we want to encrypt the message m = 7, c = me mod n = 73 mod 33 = 343 mod 33 = 13. Hence the ciphertext c = 13. //double decrypt = Math.Pow(ciphertext, d) % n; return ciphertext; } int main() { char plaintext[80],str[80]; cout<<" enter the text you want to encrpt"; cin.get(plaintext,79); int l =strlen(plaintext); for ( int i =0 ; i<l ; i++) { char s = plaintext[i]; str[i]=REncryptText(s); } for ( int i =0 ; i<l ; i++) { cout<<"the encryption of string"<<endl; cout<<str[i]; } return 0; }

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  • Approaches for Content-based Item Recommendations

    - by PartlyCloudy
    Hello, I'm currently developing an application where I want to group similar items. Items (like videos) can be created by users and also their attributes can be altered or extended later (like new tags). Instead of relying on users' preferences as most collaborative filtering mechanisms do, I want to compare item similarity based on the items' attributes (like similar length, similar colors, similar set of tags, etc.). The computation is necessary for two main purposes: Suggesting x similar items for a given item and for clustering into groups of similar items. My application so far is follows an asynchronous design and I want to decouple this clustering component as far as possible. The creation of new items or the addition of new attributes for an existing item will be advertised by publishing events the component can then consume. Computations can be provided best-effort and "snapshotted", which means that I'm okay with the best result possible at a given point in time, although result quality will eventually increase. So I am now searching for appropriate algorithms to compute both similar items and clusters. At important constraint is scalability. Initially the application has to handle a few thousand items, but later million items might be possible as well. Of course, computations will then be executed on additional nodes, but the algorithm itself should scale. It would also be nice if the algorithm supports some kind of incremental mode on partial changes of the data. My initial thought of comparing each item with each other and storing the numerical similarity sounds a little bit crude. Also, it requires n*(n-1)/2 entries for storing all similarities and any change or new item will eventually cause n similarity computations. Thanks in advance! UPDATE tl;dr To clarify what I want, here is my targeted scenario: User generate entries (think of documents) User edit entry meta data (think of tags) And here is what my system should provide: List of similar entries to a given item as recommendation Clusters of similar entries Both calculations should be based on: The meta data/attributes of entries (i.e. usage of similar tags) Thus, the distance of two entries using appropriate metrics NOT based on user votings, preferences or actions (unlike collaborative filtering). Although users may create entries and change attributes, the computation should only take into account the items and their attributes, and not the users associated with (just like a system where only items and no users exist). Ideally, the algorithm should support: permanent changes of attributes of an entry incrementally compute similar entries/clusters on changes scale something better than a simple distance table, if possible (because of the O(n²) space complexity)

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  • How do I measure the size of a TextBlock in WPF before it is rendered?

    - by Scott Whitlock
    I have a WPF DataTemplate with two TextBlock controls (stacked) and then some other elements underneath. Due to some complicated layout code, I need to know the height of the two TextBlock elements so that I can draw some fancy connector lines, and line up other controls, etc. If I know the text that's going into the TextBlocks, and I know the font, etc., is there some way I can compute or measure the height of these TextBlocks without actually rendering them?

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  • Worst Case number of rotations for BST to AVL algorithm?

    - by spacker_lechuck
    I have a basic algorithm below and I know that the worst case input BST is one that has degenerated to a linked list from inserts to only one side. How would I compute the worst case complexity in terms of number of rotations for this BST to AVL conversion algorithm? IF tree is right heavy { IF tree's right subtree is left heavy { Perform Double Left rotation } ELSE { Perform Single Left rotation } } ELSE IF tree is left heavy { IF tree's left subtree is right heavy { Perform Double Right rotation } ELSE { Perform Single Right rotation } }

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  • extendible hashing

    - by Phenom
    I need to make a program that shows the hash value of a given key, using extendible hashing. In extendible hashing, I know that the buckets split and directories change. So if I make my program, do I have to already know things like if the bucket it hashes to is filled, or do I not have to worry about those things and just compute a hash value based on the key?

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  • O(log n) algorithm for merging lists and computing rank?

    - by Eternal Learner
    Given two sorted lists, each containing n real numbers, is there a O(log?n) time algorithm to compute the element of rank i (where i coresponds to index in increasing order) in the union of the two lists, assuming the elements of the two lists are distinct? I can think of using a Merge procedure to merge the 2 lists and then find the A[i] element in constant time. But the Merge would take O(n) time. How do we solve it in O(log n) time?

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  • doing arithmetic upto two significant figures in Python?

    - by user248237
    I have two floats in Python that I'd like to subtract, i.e. v1 = float(value1) v2 = float(value2) diff = v1 - v2 I want "diff" to be computed upto two significant figures, that is compute it using %.2f of v1 and %.2f of v2. How can I do this? I know how to print v1 and v2 up to two decimals, but not how to do arithmetic like that. thanks.

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  • Is there a way to set a handler function for when a set of events has happened in JavaScript?

    - by allyourcode
    eg I have two concurrent AJAX requests, and I need the result from both to compute a third result. I'm using the Prototype library, so it might look something like this: var r1 = new Ajax.Request(url1, ...); var r2 = new Ajax.Request(url2, ...); function on_both_requests_complete(resp1, resp2) { ... } One way would be to use polling, but I'm thinking there must be a better way.

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  • Floating point computer - Trouble with getting back correct results

    - by Francisco P.
    Having trouble with a challenge. Let's say I have a theoretical, base 10, floating point calculator with the following characteristics Only 3 digits for mantissa 1 digit for exponent Sign for mantissa and exponent How would this machine compute the following? 300 + \sum_{i=1}^{100} 0.2 The correct result is 320. The machine's result is 300. But why? Can't get where the 20 goes goes missing... Thanks for your time.

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  • R: optimal way of computing the "product" of two vectors

    - by Musa
    Hi, Let's assume that I have a vector r <- rnorm(4) and a matrix W of dimension 20000*200 for example: W <- matrix(rnorm(20000*200),20000,200) I want to compute a new matrix M of dimension 5000*200 such that m11 <- r%*%W[1:4,1], m21 <- r%*%W[5:8,1], m12 <- r%*%W[1:4,2] etc. (i.e. grouping rows 4-by-4 and computing the product). What's the optimal (speed,memory) way of doing this? Thanks in advance.

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  • recursive cumulative sums

    - by user1816377
    I need to write a program that compute cumulative sums from a list of numbers with def but ONLY with recursion. I did it, but now I need to write the same program without using the method sum, but no success so far. Any idea? my code: def rec_cumsum(numbers): ''' Input: numbers - a list of numbers, Output: a list of cumulative sums of the numbers''' if len(numbers)==0: return numbers return rec_cumsum(numbers[:-1])+ [sum(numbers)] input: 1 [1,2,3] 2 [2, 2, 2, 3] output: 1 [1,3,6] 2 [2, 4, 6, 9]

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  • Why does (360 / 24) / 60 = 0 ... in Java

    - by Ankur
    I am trying to compute (360 / 24) / 60 I keep getting the answer 0.0 when I should get 0.25 In words: I want to divide 360 by 24 and then divide the result by 60 public class Divide { public static void main(String[] args){ float div = ((360 / 24) / 60); System.out.println(div); } } This prints out: 0.0 Why is that? Am I doing something really stupid, or is there a good reason for this

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  • Number of the different elements in an array.

    - by AB
    Is it possible to compute the number of the different elements in an array in linear time and constant space? Let us say it's an array of long integers, and you can not allocate an array of length sizeof(long). P.S. Not homework, just curious. I've got a book that sort of implies that it is possible.

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  • How does the Cloud compare to Colocation? And development too

    - by David
    Currently I/we run a SaaS web application where each subscriber has their own physical instance of the application in addition to their own database. The setup has each web application instance deployed on two different IIS boxes both for load-balancing and redundancy (the machines have their Windows Update install times 12 hours apart, for example). Databases are mirrored on two different SQL Server 2012 machines with AlwaysOn for uptime. I don't make use of SQL Server clustering (as it doesn't provide storage-level failover: we don't have a shared storage box). Because it's a Windows setup it means there are two Domain Controllers (we cheat: they're both Mac Minis, 17W each, which keeps our colo power costs low). Finally there's also an Exchange server (Mailbox, Hub Transport and Client Access). One of the SQL Servers also doubles-up as an Exchange Hub Transport. Running costs are about $700 a month for our quarter-rack colocation (which includes power and peering/transfer), then there's about $150 a month for SPLA licensing, so $850 a month in total. Then there's the hard-to-quantify cost of administration, but I reckon I spend a couple of hours a week checking-in on the servers: reviewing event logs, etc. I keep getting bombarded by ads and manufactured news stories about how great "the cloud" is. Back in 2008 when the cloud was taking off I was reading up about the proper "cloud" services like Google AppEngine, where you write in Python against Google's API and that's how they scale your application across servers and also use their database provider for scaling storage. Simple enough to understand. Then came along Amazon, and I understand how Amazon Storage works, but I'm not sure how Amazon Compute works: web application pages don't take much CPU time to compute, how do you even quantify usage anyway? Finally, RackSpace gets in the act and now I'm really confused. RackSpace advertise "Cloud" SQL Server 2012 available for about "$0.70 per hour", going by how they advertise it I thought the "hour" meant the sum of CPU time, IO blocking time, maybe time spent transferring data, so for a low-intensity application that works out pretty cheap then? Nope. I went on to a Sales Chat window and spoke to one of their advisors. They told me the $0.70/hour was actually for every hour the SQL Server is running... but who wants a SQL Server for only a few hours? You're going to need it available 24 hours a day for months on end. $0.70 * 24 * 31 works out at $520 a month, which is rediculously expensive for SQL Server. An SPLA license for SQL Server is only $50 a month or so. That $520 a month does not include "fanatical support", and you also need to stack on top the costs of the host Windows server instance too. From what I can tell, Rackspace's "Cloud" products seem like like an cynical rebranding of an overpriced VPS service, but priced by the hour. I have the same confusion about Windows Azure which uses similar terms to describe the products available, but I think that's because Azure offers both traditional shared webhosting in addition to their own APIs you can target for scalable applications.

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  • Deferred rendering with VSM - Scaling light depth loses moments

    - by user1423893
    I'm calculating my shadow term using a VSM method. This works correctly when using forward rendered lights but fails with deferred lights. // Shadow term (1 = no shadow) float shadow = 1; // [Light Space -> Shadow Map Space] // Transform the surface into light space and project // NB: Could be done in the vertex shader, but doing it here keeps the // "light shader" abstraction and doesn't limit the number of shadowed lights float4x4 LightViewProjection = mul(LightView, LightProjection); float4 surf_tex = mul(position, LightViewProjection); // Re-homogenize // 'w' component is not used in later calculations so no need to homogenize (it will equal '1' if homogenized) surf_tex.xyz /= surf_tex.w; // Rescale viewport to be [0,1] (texture coordinate system) float2 shadow_tex; shadow_tex.x = surf_tex.x * 0.5f + 0.5f; shadow_tex.y = -surf_tex.y * 0.5f + 0.5f; // Half texel offset //shadow_tex += (0.5 / 512); // Scaled distance to light (instead of 'surf_tex.z') float rescaled_dist_to_light = dist_to_light / LightAttenuation.y; //float rescaled_dist_to_light = surf_tex.z; // [Variance Shadow Map Depth Calculation] // No filtering float2 moments = tex2D(ShadowSampler, shadow_tex).xy; // Flip the moments values to bring them back to their original values moments.x = 1.0 - moments.x; moments.y = 1.0 - moments.y; // Compute variance float E_x2 = moments.y; float Ex_2 = moments.x * moments.x; float variance = E_x2 - Ex_2; variance = max(variance, Bias.y); // Surface is fully lit if the current pixel is before the light occluder (lit_factor == 1) // One-tailed inequality valid if float lit_factor = (rescaled_dist_to_light <= moments.x - Bias.x); // Compute probabilistic upper bound (mean distance) float m_d = moments.x - rescaled_dist_to_light; // Chebychev's inequality float p = variance / (variance + m_d * m_d); p = ReduceLightBleeding(p, Bias.z); // Adjust the light color based on the shadow attenuation shadow *= max(lit_factor, p); This is what I know for certain so far: The lighting is correct if I do not try and calculate the shadow term. (No shadows) The shadow term is correct when calculated using forward rendered lighting. (VSM works with forward rendered lights) With the current rescaled light distance (lightAttenuation.y is the far plane value): float rescaled_dist_to_light = dist_to_light / LightAttenuation.y; The light is correct and the shadow appears to be zoomed in and misses the blurring: When I do not rescale the light and use the homogenized 'surf_tex': float rescaled_dist_to_light = surf_tex.z; the shadows are blurred correctly but the lighting is incorrect and the cube model is no longer lit Why is scaling by the far plane value (LightAttenuation.y) zooming in too far? The only other factor involved is my world pixel position, which is calculated as follows: // [Position] float4 position; // [Screen Position] position.xy = input.PositionClone.xy; // Use 'x' and 'y' components already homogenized for uv coordinates above position.z = tex2D(DepthSampler, texCoord).r; // No need to homogenize 'z' component position.z = 1.0 - position.z; position.w = 1.0; // 1.0 = position.w / position.w // [World Position] position = mul(position, CameraViewProjectionInverse); // Re-homogenize position (xyz AND w, otherwise shadows will bend when camera is close) position.xyz /= position.w; position.w = 1.0; Using the inverse matrix of the camera's view x projection matrix does work for lighting but maybe it is incorrect for shadow calculation? EDIT: Light calculations for shadow including 'dist_to_light' // Work out the light position and direction in world space float3 light_position = float3(LightViewInverse._41, LightViewInverse._42, LightViewInverse._43); // Direction might need to be negated float3 light_direction = float3(-LightViewInverse._31, -LightViewInverse._32, -LightViewInverse._33); // Unnormalized light vector float3 dir_to_light = light_position - position; // Direction from vertex float dist_to_light = length(dir_to_light); // Normalise 'toLight' vector for lighting calculations dir_to_light = normalize(dir_to_light); EDIT2: These are the calculations for the moments (depth) //============================================= //---[Vertex Shaders]-------------------------- //============================================= DepthVSOutput depth_VS( float4 Position : POSITION, uniform float4x4 shadow_view, uniform float4x4 shadow_view_projection) { DepthVSOutput output = (DepthVSOutput)0; // First transform position into world space float4 position_world = mul(Position, World); output.position_screen = mul(position_world, shadow_view_projection); output.light_vec = mul(position_world, shadow_view).xyz; return output; } //============================================= //---[Pixel Shaders]--------------------------- //============================================= DepthPSOutput depth_PS(DepthVSOutput input) { DepthPSOutput output = (DepthPSOutput)0; // Work out the depth of this fragment from the light, normalized to [0, 1] float2 depth; depth.x = length(input.light_vec) / FarPlane; depth.y = depth.x * depth.x; // Flip depth values to avoid floating point inaccuracies depth.x = 1.0f - depth.x; depth.y = 1.0f - depth.y; output.depth = depth.xyxy; return output; } EDIT 3: I have tried the folloiwng: float4 pp; pp.xy = input.PositionClone.xy; // Use 'x' and 'y' components already homogenized for uv coordinates above pp.z = tex2D(DepthSampler, texCoord).r; // No need to homogenize 'z' component pp.z = 1.0 - pp.z; pp.w = 1.0; // 1.0 = position.w / position.w // Determine the depth of the pixel with respect to the light float4x4 LightViewProjection = mul(LightView, LightProjection); float4x4 matViewToLightViewProj = mul(CameraViewProjectionInverse, LightViewProjection); float4 vPositionLightCS = mul(pp, matViewToLightViewProj); float fLightDepth = vPositionLightCS.z / vPositionLightCS.w; // Transform from light space to shadow map texture space. float2 vShadowTexCoord = 0.5 * vPositionLightCS.xy / vPositionLightCS.w + float2(0.5f, 0.5f); vShadowTexCoord.y = 1.0f - vShadowTexCoord.y; // Offset the coordinate by half a texel so we sample it correctly vShadowTexCoord += (0.5f / 512); //g_vShadowMapSize This suffers the same problem as the second picture. I have tried storing the depth based on the view x projection matrix: output.position_screen = mul(position_world, shadow_view_projection); //output.light_vec = mul(position_world, shadow_view); output.light_vec = output.position_screen; depth.x = input.light_vec.z / input.light_vec.w; This gives a shadow that has lots surface acne due to horrible floating point precision errors. Everything is lit correctly though. EDIT 4: Found an OpenGL based tutorial here I have followed it to the letter and it would seem that the uv coordinates for looking up the shadow map are incorrect. The source uses a scaled matrix to get the uv coordinates for the shadow map sampler /// <summary> /// The scale matrix is used to push the projected vertex into the 0.0 - 1.0 region. /// Similar in role to a * 0.5 + 0.5, where -1.0 < a < 1.0. /// <summary> const float4x4 ScaleMatrix = float4x4 ( 0.5, 0.0, 0.0, 0.0, 0.0, -0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.5, 0.5, 1.0 ); I had to negate the 0.5 for the y scaling (M22) in order for it to work but the shadowing is still not correct. Is this really the correct way to scale? float2 shadow_tex; shadow_tex.x = surf_tex.x * 0.5f + 0.5f; shadow_tex.y = surf_tex.y * -0.5f + 0.5f; The depth calculations are exactly the same as the source code yet they still do not work, which makes me believe something about the uv calculation above is incorrect.

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  • Movement prediction for non-shooters

    - by ShadowChaser
    I'm working on an isometric 2D game with moderate-scale multiplayer, approximately 20-30 players connected at once to a persistent server. I've had some difficulty getting a good movement prediction implementation in place. Physics/Movement The game doesn't have a true physics implementation, but uses the basic principles to implement movement. Rather than continually polling input, state changes (ie/ mouse down/up/move events) are used to change the state of the character entity the player is controlling. The player's direction (ie/ north-east) is combined with a constant speed and turned into a true 3D vector - the entity's velocity. In the main game loop, "Update" is called before "Draw". The update logic triggers a "physics update task" that tracks all entities with a non-zero velocity uses very basic integration to change the entities position. For example: entity.Position += entity.Velocity.Scale(ElapsedTime.Seconds) (where "Seconds" is a floating point value, but the same approach would work for millisecond integer values). The key point is that no interpolation is used for movement - the rudimentary physics engine has no concept of a "previous state" or "current state", only a position and velocity. State Change and Update Packets When the velocity of the character entity the player is controlling changes, a "move avatar" packet is sent to the server containing the entity's action type (stand, walk, run), direction (north-east), and current position. This is different from how 3D first person games work. In a 3D game the velocity (direction) can change frame to frame as the player moves around. Sending every state change would effectively transmit a packet per frame, which would be too expensive. Instead, 3D games seem to ignore state changes and send "state update" packets on a fixed interval - say, every 80-150ms. Since speed and direction updates occur much less frequently in my game, I can get away with sending every state change. Although all of the physics simulations occur at the same speed and are deterministic, latency is still an issue. For that reason, I send out routine position update packets (similar to a 3D game) but much less frequently - right now every 250ms, but I suspect with good prediction I can easily boost it towards 500ms. The biggest problem is that I've now deviated from the norm - all other documentation, guides, and samples online send routine updates and interpolate between the two states. It seems incompatible with my architecture, and I need to come up with a better movement prediction algorithm that is closer to a (very basic) "networked physics" architecture. The server then receives the packet and determines the players speed from it's movement type based on a script (Is the player able to run? Get the player's running speed). Once it has the speed, it combines it with the direction to get a vector - the entity's velocity. Some cheat detection and basic validation occurs, and the entity on the server side is updated with the current velocity, direction, and position. Basic throttling is also performed to prevent players from flooding the server with movement requests. After updating its own entity, the server broadcasts an "avatar position update" packet to all other players within range. The position update packet is used to update the client side physics simulations (world state) of the remote clients and perform prediction and lag compensation. Prediction and Lag Compensation As mentioned above, clients are authoritative for their own position. Except in cases of cheating or anomalies, the client's avatar will never be repositioned by the server. No extrapolation ("move now and correct later") is required for the client's avatar - what the player sees is correct. However, some sort of extrapolation or interpolation is required for all remote entities that are moving. Some sort of prediction and/or lag-compensation is clearly required within the client's local simulation / physics engine. Problems I've been struggling with various algorithms, and have a number of questions and problems: Should I be extrapolating, interpolating, or both? My "gut feeling" is that I should be using pure extrapolation based on velocity. State change is received by the client, client computes a "predicted" velocity that compensates for lag, and the regular physics system does the rest. However, it feels at odds to all other sample code and articles - they all seem to store a number of states and perform interpolation without a physics engine. When a packet arrives, I've tried interpolating the packet's position with the packet's velocity over a fixed time period (say, 200ms). I then take the difference between the interpolated position and the current "error" position to compute a new vector and place that on the entity instead of the velocity that was sent. However, the assumption is that another packet will arrive in that time interval, and it's incredibly difficult to "guess" when the next packet will arrive - especially since they don't all arrive on fixed intervals (ie/ state changes as well). Is the concept fundamentally flawed, or is it correct but needs some fixes / adjustments? What happens when a remote player stops? I can immediately stop the entity, but it will be positioned in the "wrong" spot until it moves again. If I estimate a vector or try to interpolate, I have an issue because I don't store the previous state - the physics engine has no way to say "you need to stop after you reach position X". It simply understands a velocity, nothing more complex. I'm reluctant to add the "packet movement state" information to the entities or physics engine, since it violates basic design principles and bleeds network code across the rest of the game engine. What should happen when entities collide? There are three scenarios - the controlling player collides locally, two entities collide on the server during a position update, or a remote entity update collides on the local client. In all cases I'm uncertain how to handle the collision - aside from cheating, both states are "correct" but at different time periods. In the case of a remote entity it doesn't make sense to draw it walking through a wall, so I perform collision detection on the local client and cause it to "stop". Based on point #2 above, I might compute a "corrected vector" that continually tries to move the entity "through the wall" which will never succeed - the remote avatar is stuck there until the error gets too high and it "snaps" into position. How do games work around this?

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