i am struggling to figure out how to create the Takashi Murikami flower using shapes, bezier curves, vertecies and shapes. this is a little above and beyond for the class that I am taking, and i am really hoping there is a way to do it. Either just one large flower of his in the center or a way to create a repeating pattern of flowers. Any help would be very very much appreciated! thanks in advance

I took advantage of colorMode(HSB, 12, 100, 100) for this:

This is an achievable exercise if you put some work into it.

Initially I did not use math and placed shapes manually… you will learn a lot about the method and it’s parameters doing this and can then apply the math if desired.

I used tangents to circles once I applied the math to a petal:

I did a lot of exploration with this including arc(), bezierVertex(), etc. and came up with a few solutions and a custom shape.

Effectively you are trying to draw a composite shape - a shape made from several others in 2D. In computer graphics this is a common programing task so I am going to provide a fairly detailed answer but with minmal code - after all there should be some challenge

When creating a composite shape there are a number of extremely important methods that you need to become familiar with. These methods are not used to render a shape but rather transform the XY axis used to position the shapes. They are translate(x,y), rotate(angle), push() and pop() and you should look these up in the reference if you are unfamiliar with them.

Stage 1 : Modular design
We can break this problem into a number of tasks and sub tasks

Draw Flower
|-- draw petals
| |-- draw a petal (repeat for each petal
|-- draw face
|-- draw face background
|-- draw mouth
|-- draw eyes
|-- draw left eye
|-- draw right eye

We can create a series of functions for each task this bit shows the first three tasks with basic code to manage transformations.

void drawFlower(float x, float y) {
push(); // save the transfprmatiom matrix
translate(x, y); // move axis to centre of flower to draw
drawPetals();
/* Now do the rest
|-- draw face
|-- draw face background
|-- draw mouth
|-- draw eyes
|-- draw left eye
|-- draw right eye
*/
pop(); // restore the transfprmatiom matrix
}
void drawPetals() {
push();
float deltaAngle = TWO_PI/12;
for (int i = 0; i < 12; i++) {
drawPetal();
rotate(deltaAngle);
}
pop();
}
void drawPetal() {
// push & pop not required because rotation is cumulative
// and controlled in calling function
// Some maths needed here LOL
}

Drawing the petal

The code for drawing a single petal is the same for every petal ,we simply rotate the axis for drawing each petal.

In the image the point O has the coordinates [0, 0]. If we define the size of the petal (r) as the length \overrightarrow{OA} then we can calculate the coordinates for A, B and C as
A = [r .cos(ang/2), r.sin(ang/2)]
B = [r .cos(ang/2), -r.sin(ang/2)]
C = [r .cos(ang/2), 0]
and finally the radius of the semi-circle \overrightarrow{CD} equals r.sin(ang/2)

Knowing these values the patal can be draw using triangle(...) and arc(...) methods.