Abstract: Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies. Displacements caused by reaction forces necessary to ensure that the bodies comply with the position constraints can be calculated and can be done iteratively by updating equations defining the reaction forces and the displacements such that the computation time and memory resources required to perform the calculations is linearly dependent upon the number of bodies and the number of contacts and joints between the bodies.

Abstract: Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies. Displacements caused by reaction forces necessary to ensure that the bodies comply with the position constraints can be calculated and can be done iteratively by updating equations defining the reaction forces and the displacements such that the computation time and memory resources required to perform the calculations is linearly dependent upon the number of bodies and the number of contacts and joints between the bodies. Computational requirements and memory requirements are reduced further by performing the calculations using vector operations.

Abstract: A respective weighting value is calculated for each texel in a texture map that is to be used to render a 3D computer model, the weighting value being calculated in dependence upon the red, green and blue values of the texel. Each weighting value is stored as an alpha value in the alpha channel for the corresponding texel in the texture map. During rendering, the texture map is rendered onto a polygon to generate R, G, B pixel values in the frame buffer together with a respective weighting value for each pixel comprising the weighting value calculated for the corresponding texel in the texture map, which is stored in the alpha channel for the pixel. A darkmap is rendered onto the polygon by subtracting from the pixel values in the frame buffer the darkmap values modulated by the frame buffer alpha values. The texel weighting values are calculated so that they have properties which result in a realistic image being generated.

Abstract: Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies. Displacements caused by reaction forces necessary to ensure that the bodies comply with the position constraints can be calculated and can be done iteratively by updating equations defining the reaction forces and the displacements such that the computation time and memory resources required to perform the calculations is linearly dependent upon the number of bodies and the number of contacts and joints between the bodies. Computational requirements and memory requirements are reduced further by performing the calculations using vector operations.

Abstract: Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies.

Abstract: Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies. Displacements caused by reaction forces necessary to ensure that the bodies comply with the position constraints can be calculated and can be done iteratively by updating equations defining the reaction forces and the displacements such that the computation time and memory resources required to perform the calculations is linearly dependent upon the number of bodies and the number of contacts and joints between the bodies.

Abstract: A respective weighting value is calculated for each texel in a texture map that is to be used to render a 3D computer model, the weighting value being calculated in dependence upon the red, green and blue values of the texel. Each weighting value is stored as an alpha value in the alpha channel for the corresponding texel in the texture map. During rendering, the texture map is rendered onto a polygon to generate R, G, B pixel values in the frame buffer together with a respective weighting value for each pixel comprising the weighting value calculated for the corresponding texel in the texture map, which is stored in the alpha channel for the pixel. A darkmap is rendered onto the polygon by subtracting from the pixel values in the frame buffer the darkmap texel weighting values are calculated so that they have properties which result in a realistic image being generated.