API design guidelines

The following guidelines are meant to make the user experience more pleasant. They are aimed to help the user make use of existing tools and increase productivity. As a first guideline, keep in mind that somebody other than you will use your code.

Object orientation

Object orientation is a design approach that attempts to model real world objects in the code.
Try to think in objects.
Make use of the visibility of objects.
Hide your implementation from the user.
On the other hand, not every class needs to have a set of private data members with a full-blown set of Setters and Getters. It is ok to have a class with only public data members.
Rule: What belongs together logically should be handled together
Example:

class SimpleParameterClass {
public int spaceX;
public double tanPolarPhi;
public float cosLine1Line2;
}
...
SimpleParameterClass parms = new SimpleParameterClass();
parms.spaceX = 17; // you can simply set it
...
System.out.printf("%f", parms.cosLine1Line2); // or get it -- no need for encapsulation

double[] parms = new double[] {17, 3.4, 2.5};
parms[2] = 2.5; // Which one is it ???

Optimization

Optimization obfuscates code. It also forces you to change your intuitive approach.
Rule: First, write your code. Then profile it. Then, if necessary, optimize it.

Status codes

In the good old Fortran and C days, obscure statuscodes and bitfields were common sight. While it is true that your code should be optimized at the persistence level, make sure you include definitions of your statuscodes in the API. The use of Enum, EnumSet and EnumMap is encouraged.

enum MyClassFlags {doThingX, doThingY, doThingZ};
    class MyClass {
    MyClassFlags flags;
    void setFlags(EnumSet f) {flags = f;}
}
...
EnumSet<MyClassFlags> myFlags = new EnumSet<MyClassFlags>();
myFlags.add(MyClassFlags.doThingX); // yes, it is more verbose. That is a good thing !
MyClass c;
c.setFlags(myFlags);

class Obscure {
    int obscureFlag;
    void setObscureFlag(int o) {obscureFlag = o;}
}
...
Obscure o
o.setObscureFlag(3);

"Overloaded Operators"

The Java language does not support the concept of overloading operators. If you decide to write a custom operator for your class, consider the following:

vec1.add(vec2);

import static x.y.add; add(vec1, vec2);

vec1.add(vec1, vec2);

Using strings to access parameters

Strings should be used for input/output operations only. They are slow to parse and cannot be checked for typos at compile time.
Using them to set flags and parameters is not recommended.
See the section about status codes above. If you need to set different parameters with the same function, use an EnumMap