Figure 3 - uploaded by Alejandro L. Garcia
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(Left) Character demonstrating the Law of Inertia by standing on a bus when it comes to a sudden stop. (Right) This character is seated when the bus stops; notice how her hair flies forward due to the Law of Inertia.
Source publication
An understanding of physics is essential for creating believable animated motion. Many basic concepts in animation (such as follow-through, drag, and weight shift) are clearer when considered in the context of basic mechanics.
This course was developed with support from the National Science Foundation by Alejandro Garcia, who was on leave at the De...
Contexts in source publication
Context 1
... rock sitting on a table has two forces on it: gravity pulling downward and the table surface pushing upward. These two forces balance each other. A bowling ball rolling on a smooth floor has a similar pair of balanced forces (gravity and the floor). If there's no other force on the bowling ball then there's no unbalanced forces so it moves with constant velocity. Same with the rock, it's speed just happens to be zero. At first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let's take a simple example of a character standing on a bus (see Figure 3). When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving and by the Law of Inertia, he'll continue moving until a force acts to stop him (such as when he hits the floor). Another example is seen in the follow-through (forward motion) of a seated passenger's hair (see Figure 3 again) when the bus hits the ...
Context 2
... rock sitting on a table has two forces on it: gravity pulling downward and the table surface pushing upward. These two forces balance each other. A bowling ball rolling on a smooth floor has a similar pair of balanced forces (gravity and the floor). If there's no other force on the bowling ball then there's no unbalanced forces so it moves with constant velocity. Same with the rock, it's speed just happens to be zero. At first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let's take a simple example of a character standing on a bus (see Figure 3). When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving and by the Law of Inertia, he'll continue moving until a force acts to stop him (such as when he hits the floor). Another example is seen in the follow-through (forward motion) of a seated passenger's hair (see Figure 3 again) when the bus hits the ...
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... if Mr. Alpha punches with 100 pounds of force towards the left then there's an equal force of 100 pounds on his fist towards the right. Since forces change momentum the action force causes the Mr. Beta's head to start moving towards the left while the reaction force changes the momentum of Mr. Alpha's fist, possibly bringing it to a stop. To animate this scene successfully it's essential to match the action and reaction. A common mistake is to focus on animating Mr. Beta's motion while neglecting the reaction that must simultaneously be occurring on Mr. Alpha. ¶ It doesn't matter which force is labeled "action" and which one is "reaction"; you can always switch the names since they're symmetric. Judging the effect of action-reaction is complicated by the fact that there's usually several action forces to be considered. Take the simple case of a man pushing a rock (see Figure 13). The man exerts a force on the rock so the rock exerts a force back on him. If he was on roller skates he'd move backwards and the rock would move forward. But he's barefoot so there's another set of action-reaction forces: he also pushes back on the ground and the ground pushes him forward. In order for him to push the rock forward the force exerted by his legs cannot be less than the force exerted by his arms. These actions and reactions have to appear to match in order to animate this scene ...
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... consider each part of this statement. First, the action and the reaction are a pair of matched forces. For example, suppose Mr. Alpha punches Mr. Beta (see Figure 13). The action is the force of Mr. Alpha's fist hitting Mr. Beta's face so the reaction is the force of Mr. Beta's face pushing back on Mr. Alpha's fist. ¶ Second, these two forces are instantaneous so if Mr. Beta punches back that's not the reaction, that's a new ...
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... by an “unbalanced force.” The simplest form of the Law of Inertia is that an object in motion remains in motion unless acted on by a force, for example, an asteroid in deep space moves with constant velocity. But unless you animated a shot in Wall-E it’s unlikely you’ve encounter a situation where there’s absolutely no forces. A rock sitting on a table has two forces on it: gravity pulling downward and the table surface pushing upward. These two forces balance each other. A bowling ball rolling on a smooth floor has a similar pair of balanced forces (gravity and the floor). If there’s no other force on the bowling ball then there’s no unbalanced forces so it moves with constant velocity. Same with the rock, it’s speed just happens to be zero. At first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let’s take a simple example of a character standing on a bus (see Figure 3). When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving and by the Law of Inertia, he’ll continue moving until a force acts to stop him (such as when he hits the floor). Another example is seen in the follow-through (forward motion) of a seated passenger’s hair (see Figure 3 again) when the bus hits the brakes. A corollary of the Law of Inertia is that a character at rest will remain at rest until acted on by an unbalanced force. If the bus suddenly accelerates forward then our standing character falls on his back (see Figure 4) and the seated passenger’s hair seems to drag behind. As fellow passengers it seems to us as if there’s a force pulling everything backwards but that’s because we’re moving with the bus. A stationary observer standing outside the bus would realize that the poor chap that’s falling has the bus moving out from under him (see Figure 5). This reminds us that you have to be careful to include the effect of the camera’s motion, especially when the camera is accelerating. Finally, the Law of Inertia also explains the drag and outward “centrifugal” force ...
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... by an “unbalanced force.” The simplest form of the Law of Inertia is that an object in motion remains in motion unless acted on by a force, for example, an asteroid in deep space moves with constant velocity. But unless you animated a shot in Wall-E it’s unlikely you’ve encounter a situation where there’s absolutely no forces. A rock sitting on a table has two forces on it: gravity pulling downward and the table surface pushing upward. These two forces balance each other. A bowling ball rolling on a smooth floor has a similar pair of balanced forces (gravity and the floor). If there’s no other force on the bowling ball then there’s no unbalanced forces so it moves with constant velocity. Same with the rock, it’s speed just happens to be zero. At first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let’s take a simple example of a character standing on a bus (see Figure 3). When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving and by the Law of Inertia, he’ll continue moving until a force acts to stop him (such as when he hits the floor). Another example is seen in the follow-through (forward motion) of a seated passenger’s hair (see Figure 3 again) when the bus hits the brakes. A corollary of the Law of Inertia is that a character at rest will remain at rest until acted on by an unbalanced force. If the bus suddenly accelerates forward then our standing character falls on his back (see Figure 4) and the seated passenger’s hair seems to drag behind. As fellow passengers it seems to us as if there’s a force pulling everything backwards but that’s because we’re moving with the bus. A stationary observer standing outside the bus would realize that the poor chap that’s falling has the bus moving out from under him (see Figure 5). This reminds us that you have to be careful to include the effect of the camera’s motion, especially when the camera is accelerating. Finally, the Law of Inertia also explains the drag and outward “centrifugal” force ...
Context 7
... first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let's take a simple example of a character standing on a bus (see Figure 3). When the bus suddenly stops the character goes flying forward. ...
Context 8
... the bus hit the brakes he was moving and by the Law of Inertia, he'll continue moving until a force acts to stop him (such as when he hits the floor). Another example is seen in the follow-through (forward motion) of a seated passenger's hair (see Figure 3 again) when the bus hits the brakes. ...
Context 9
... the action and the reaction are a pair of matched forces. For example, suppose Mr. Alpha punches Mr. Beta (see Figure 13). The action is the force of Mr. Alpha's fist hitting Mr. Beta's face so the reaction is the force of Mr. Beta's face pushing back on Mr. Alpha's fist. ...
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Human and animal presence in natural landscapes is initially revealed by the immediate impact of their locomotion, from footprints to crushed grass. In this work, we present an approach to model the effects of virtual characters on natural terrains, focusing on the impact of human locomotion. We introduce a lightweight solution to compute accurate foot placement on uneven ground and infer dynamic foot pressure from kinematic animation data and the mass of the character. A ground and vegetation model enables us to effectively simulate the local impact of locomotion on soft soils and plants over time, resulting in the formation of visible paths. As our results show, we can parameterize various soil materials and vegetation types validated with real-world data. Our method can be used to significantly increase the realism of populated natural landscapes and the sense of presence in virtual applications and games.
... This weight ratio can be intuitively seen as a way to split the contribution of the character weight between a left and right side that adapts to its posture (Garcia, 2012) and is therefore a value that is re-computed at each frame of the animation. ...
When we move on snow, sand, or mud, the ground deforms under our feet, immediately affecting our gait. We propose a physically based model for computing such interactions in real time, from only the kinematic motion of a virtual character. The force applied by each foot on the ground during contact is estimated from the weight of the character, its current balance, the foot speed at the time of contact, and the nature of the ground. We rely on a standard stress-strain relationship to compute the dynamic deformation of the soil under this force, where the amount of compression and lateral displacement of material are, respectively, parameterized by the soil's Young modulus and Poisson ratio. The resulting footprint is efficiently applied to the terrain through procedural deformations of refined terrain patches, while the addition of a simple controller on top of a kinematic character enables capturing the effect of ground deformation on the character's gait. As our results show, the resulting footprints greatly improve visual realism, while ground compression results in consistent changes in the character's motion. Readily applicable to any locomotion gait and soft soil material, our real-time model is ideal for enhancing the visual realism of outdoor scenes in video games and virtual reality applications.
... This weight ratio can be intuitively seen as a way to split the contribution of the character weight between a left and right side that adapts to its posture (Garcia, 2012) and is therefore a value that is re-computed at each frame of the animation. ...
When we move on snow, sand, or mud, the ground deforms under our feet, immediately affecting our gait. We propose a physically based model for computing such interactions in real time, from only the kinematic motion of a virtual character. The force applied by each foot on the ground during contact is estimated from the weight of the character, its current balance, the foot speed at the time of contact, and the nature of the ground. We rely on a standard stress-strain relationship to compute the dynamic deformation of the soil under this force, where the amount of compression and lateral displacement of material are, respectively, parameterized by the soil’s Young modulus and Poisson ratio. The resulting footprint is efficiently applied to the terrain through procedural deformations of refined terrain patches, while the addition of a simple controller on top of a kinematic character enables capturing the effect of ground deformation on the character’s gait. As our results show, the resulting footprints greatly improve visual realism, while ground compression results in consistent changes in the character’s motion. Readily applicable to any locomotion gait and soft soil material, our real-time model is ideal for enhancing the visual realism of outdoor scenes in video games and virtual reality applications.
