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computer graphics c version phần 7

do đó, phần đường cong có thể thiên về một kết thúc hoặc khác (Hình 10-33). C tham số điều khiển tính liên tục của vector tiếp tuyến qua ranh giới của phần. Nếu c được gán một giá trị khác không, có một gián đoạn trong độ dốc của đường cong qua các biên giới phần. | Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com 10-21__ PHYSICALLY BASED MODELING A nonrigid object such as a rope a piece of cloth or a soft rubber ball can be represented with physically based modeling methods that describe the behavior of the object in terms of the interaction of external and internal forces. An accurate discription of the shape of a terry cloth towel drapped over the back of a chair is obtained by considering the effect of the chair on the fabric loops in the cloth and the interaction between the cloth threads. A common method for modeling a nonrigid object is to approximate the object with a network of point nodes with flexible connections between the nodes. One simple type of connection is a spring. Figure 10-116 shows a section of a twodimensional spring network that could be used to approximate the behavior of a sheet of rubber. Similar spring networks can be set up in three dimensions to model a rubber ball or a block of jello. For a homogeneous object we can use identical springs throughout the network. If we want the object to have different properties in different directions we can use different spring properties in different directions. When external forces are applied to a spring network the amount of stretching or compression of the individual springs depends on the value set for the spring constant k also called the force constant for the spring. Horizontal displacement X of a node position under the influence of a force F is illustrated in Fig. 10-117. If the spring is not overstretched we can closely approximate the amount of displacement X from the equilibrium position using Hooke s law A two-dimensional spring network constructed with identical spring constants Ẳ. Fs -F.r kx III-II.ỈÍ where F is the equal and opposite restoring force of the spring on the stretched node. This relationship holds also for horizontal compression of a spring by an amount X and we have similar relationships