Higher-Degree Polynomials

Caveats and Conclusions

As you use these rules, remember that I am only skimming the surface of what you can do with calculus. These rules will help you with the examples in this book. I hope that the chapters give you a solid feel for what these equations actually mean. If the equations in this appendix don't make sense, start sketching out curves and slopes and looking at the resulting numbers . You will probably get a feel for it much more quickly.

Personally, I had a better understanding of calculus once it was put into physical terms. I talk about velocity, acceleration, and other physical concepts in many of the chapters. You may find these equations easier to understand when you think of them in those terms.

In this appendix, I have presented a couple of equations that don't fit the simple rules I've laid out. You shouldn't encounter many of these forms in this book, but you might in other areas. If you do, remember Equation A.3. In the worst case, you can solve the equation for two very close points along the curve and approximate the slope using Equation A.2. In many cases, you will be computing positions in order to populate vertex data. You can derive approximate slope values from those positions . If you find yourself trying to solve these complex equations often, invest in a calculus book.