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1. ## Constraints to Jacobian

I figured it out partially, but it doesn't work for masses other than 1.0 Can you please tell me how to fix this? Mx J = new Mx(2, 4); Mx Jdot = new Mx(2, 4); Mx M = new Mx(4); vector Fext = new vector(4); vector qdot = new vector(4); vector lambda; M.Zero(); M.data[0, 0] = 1.0 / tp.mass; M.data[1, 1] = 1.0 / tp.mass; M.data[2, 2] = 1.0 / tp3.mass; M.data[3, 3] = 1.0 / tp3.mass; Fext.zero(); Fext.data[0] = 0; Fext.data[1] = body.g; Fext.data[2] = 0; Fext.data[3] = body.g; qdot.zero(); qdot.data[0] = tp.velocity.x; qdot.data[1] = tp.velocity.y; qdot.data[2] = tp3.velocity.x; qdot.data[3] = tp3.velocity.y; Jdot.Zero(); Jdot.data[0, 0] = tp.velocity.x; Jdot.data[0, 1] = tp.velocity.y; Jdot.data[1, 0] = tp.velocity.x - tp3.velocity.x; Jdot.data[1, 1] = tp.velocity.y - tp3.velocity.y; Jdot.data[1, 2] = tp3.velocity.x - tp.velocity.x; Jdot.data[1, 3] = tp3.velocity.y - tp.velocity.y; J.Zero(); J.data[0, 0] = tp.position.x; J.data[0, 1] = tp.position.y; J.data[1, 0] = tp.position.x - tp3.position.x; J.data[1, 1] = tp.position.y - tp3.position.y; J.data[1, 2] = tp3.position.x - tp.position.x; J.data[1, 3] = tp3.position.y - tp.position.y; lambda = Mx.Invert(J * M * !J) * (-Jdot * qdot - J * M * Fext); var fvec = !J * lambda;
2. ## Constraints to Jacobian

I am incline to doubt that only video games use these kind of a simulations.
3. ## Constraints to Jacobian

I think it should be done without using angles, just positions. Just like my example article solves single pendulum just with positions. BTW what kind of math is this (in my example article)? Is it vector calculus or analytical mechanics or what, can you please tell me?
4. ## Constraints to Jacobian

I don't know how to do it. Can you please derive two ﻿equality constraints for dou﻿ble pendulum﻿?
5. ## Constraints to Jacobian

I was reading this article: https://www.toptal.com/game/video-game-physics-part-iii-constrained-rigid-body-simulation and it is missing the derivation of a Jacobian. Can somebody please do the derivation of the Jacobian with two equality constraints for double pendulum? I want to simulate double pendulum by using force-based approach with system solver, not the iterative approach.
6. ## Distortion (refraction) mapping

Hello. In many games there are transparent polygons that when you look trough them they distort the image. I would like to know how this technique,mapping is called so i can search on the net. I tried: bump distortion mapping, bitmap distortion, refraction mapping but no luck. Many thanks.