Chapter 1. First-Order ODEs. Contents. 1.1 Basic Concepts. Modeling 1.2 Geometric Meaning of y’ = ƒ (x, y). Direction Fields 1.3 Separable ODEs. Modeling 1.4 Exact ODEs. Integrating Factors 1.5 Linear ODEs. Bernoulli Equation. Population Dynamics

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DON DON. S ales S ummit 2007. DON-DON. Podjetje v številkah Sedež : -Metlika Proizvodno distribucijski obrati : -Kranj -Metlika -Maribor - Kozina - Zagreb - Split

Curves. Locus of a point moving with one degree of freedom Locus of a one-dimensional parameter family of point Mathematically defined using: Explicit equations Implicit equations Parametric equations (Hermite, Bezier, B-spline). Geometric Modeling of Curves.

Curves. Path - trajectory - motion Parameterization Designing polyloops Velocity, tangent, curvature, jerk Smoothing polyloops B-spline, Bezier and 4-points subdivisions The Jarek subdivision schemes for polyloops Arc-length parameterization Tangent and curvature estimation

http:// www.ugrad.cs.ubc.ca /~cs314/Vjan2013. University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2013 Tamara Munzner. Curves. Reading. FCG Chap 15 Curves Ch 13 2nd edition. Curves. Parametric Curves. parametric form for a line:

Curves. Jim Van Verth (jim@essentialmath.com). Animation. Problem: want to replay stored set of transformations Generated by artist Generated by motion capture Two main issues Replaying position Replaying orientation. Animation of Position. Set of points representing position

CURVES. CURVES WHY?? WHAT?? PARAMETERS??. NECESSITY ARISES DUE TO PHYSICAL & GEOGRAPHICAL FEATURES NECESSARY EVIL CURVE IS A LINE OF WHICH NO PART IS STRAIGHT AND WHICH CHANGES DIRECTION WITHOUT ANGLES POSITIVE IMPEDIMENTS FOR HIGHER SPEEDS. Angle of attack. α.

Curves. Jim Van Verth (jim@essentialmath.com). Animation. Problem: want to replay stored set of transformations Generated by artist Generated by motion capture Two main issues Replaying position Replaying orientation. Animation of Position. Set of points representing position

Curves. Dr Duxbury. Quadratic graphs. In a quadratic function, the highest power of x is 2 and it is of the form y = ax 2 + bx + c. Are the following quadratic functions?. Cubic graphs. In a cubic function, the highest power of x is 3 and it is of the form y = ax 3 + bx 2 + cx + d.

Curves. Chiew-Lan Tai. Reading. Required Hearn & Baker, 8-8 – 8-10, 8-12 Foley, 11.2. Curves Before Computers. The loftsman’s or carpenter’s spline: long, narrow strip of wood or metal shaped by lead weights called “ducks” Usually gives curves with second-order continuity