package GfxLib; public class Matrix3D { // // Shared data // private static final float[][] IDENTITY_ELEMS = { {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1} }; private static Matrix3D temp1; // // Public member variables // public int ID; // // Private member variables // private float[][] m_elems; // // Class Constructors // public Matrix3D() { m_elems = new float[4][4]; this.loadIdentity(); } public Matrix3D(Matrix3D copy) { m_elems = new float[4][4]; for (int arr = 0; arr < 4; arr++) { System.arraycopy(copy.getElements()[arr], 0, m_elems[arr], 0, 4); } } public void copy(Matrix3D copy) { for (int arr = 0; arr < 4; arr++) { System.arraycopy(copy.getElements()[arr], 0, m_elems[arr], 0, 4); } } public Matrix3D(Raster r) { m_elems = new float[4][4]; this.loadIdentity(); m_elems[0][0] = r.getWidth()/2; m_elems[1][1] = r.getHeight()/2; m_elems[0][3] = r.getWidth()/2; m_elems[1][3] = r.getHeight()/2; m_elems[2][3] = 0f; m_elems[2][2] = 0f; } public Matrix3D(Raster r, float near, float far) { m_elems = new float[4][4]; this.loadIdentity(); m_elems[0][0] = r.getWidth()/2; m_elems[1][1] = r.getHeight()/2; m_elems[0][3] = r.getWidth()/2; m_elems[1][3] = r.getHeight()/2; m_elems[2][3] = 256/(far-near); m_elems[2][2] = near*256/(far-near); } // // Data access methods // public final float get(int i, int j) { return m_elems[j][i]; } public final float[][] getElements() { return m_elems; } public final void set(int i, int j, float value) { m_elems[j][i] = value; } // // Transforms // public final void compose(Matrix3D src) { float[][] newElems = { {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0} }; float[][] srcElems = src.getElements(); float[][] tempElems = m_elems; for (int j = 0; j < 4; j++) { for (int i = 0; i < 4; i++) { newElems[j][i] = tempElems[j][0] * srcElems[0][i] + tempElems[j][1] * srcElems[1][i] + tempElems[j][2] * srcElems[2][i] + tempElems[j][3] * srcElems[3][i]; } } m_elems = newElems; } public void lookAt(float eyex, float eyey, float eyez, float atx, float aty, float atz, float upx, float upy, float upz) { float lx, ly, lz, lxHat, lyHat, lzHat, lNormal; float rx, ry, rz, rxHat, ryHat, rzHat, rNormal; float ux, uy, uz, uxHat, uyHat, uzHat, uNormal; Matrix3D viewMatrix = new Matrix3D(); viewMatrix.loadIdentity(); lx = atx - eyex; ly = aty - eyey; lz = atz - eyez; lNormal = (float)Math.sqrt(lx*lx + ly*ly + lz*lz); lxHat = lx / lNormal; lyHat = ly / lNormal; lzHat = lz / lNormal; rx = (ly * upz) - (lz * upy); ry = (lz * upx) - (lx * upz); rz = (lx * upy) - (ly * upx); rNormal = (float)Math.sqrt(rx*rx + ry*ry + rz*rz); rxHat = rx / rNormal; ryHat = ry / rNormal; rzHat = rz / rNormal; ux = (ry * lz) - (rz * ly); uy = (rz * lx) - (rx * lz); uz = (rx * ly) - (ry * lx); uNormal = (float)Math.sqrt(ux*ux + uy*uy + uz*uz); uxHat = ux / uNormal; uyHat = uy / uNormal; uzHat = uz / uNormal; // Check for consistency w/ old matrix classs!!! viewMatrix.set(0, 0, rxHat); viewMatrix.set(1, 0, ryHat); viewMatrix.set(2, 0, rzHat); viewMatrix.set(3, 0, -((rxHat * eyex) + (ryHat * eyey) + (rzHat * eyez))); viewMatrix.set(0, 1, uxHat); viewMatrix.set(1, 1, uyHat); viewMatrix.set(2, 1, uzHat); viewMatrix.set(3, 1, -((uxHat * eyex) + (uyHat * eyey) + (uzHat * eyez))); viewMatrix.set(0, 2, -lxHat); viewMatrix.set(1, 2, -lyHat); viewMatrix.set(2, 2, -lzHat); viewMatrix.set(3, 2, ((lxHat * eyex) + (lyHat * eyey) + (lzHat * eyez))); this.compose(viewMatrix); } public void orthographic(float left, float right, float bottom, float top, float near, float far) { float[][] pMatrixElems; Matrix3D pMatrix; pMatrix = temp1; pMatrix.loadIdentity(); pMatrixElems = pMatrix.getElements(); pMatrixElems[0][0] = 2f/(right-left); pMatrixElems[0][3] = -(right + left)/(right-left); pMatrixElems[1][1] = 2f/(bottom-top); pMatrixElems[1][3] = -(bottom+top)/(bottom-top); pMatrixElems[2][2] = 2f/(far-near); pMatrixElems[2][3] = -(far+near)/(far-near); this.compose(pMatrix); } public void perspective(float left, float right, float bottom, float top, float near, float far) { float[][] pMatrixElems; Matrix3D pMatrix; pMatrix = temp1; pMatrix.loadIdentity(); pMatrixElems = pMatrix.getElements(); pMatrixElems[0][0] = (2f * near)/(right - left); pMatrixElems[0][2] = -(right + left)/(right-left); pMatrixElems[1][1] = (2f*near)/(bottom-top); pMatrixElems[1][2] = -(bottom+top)/(bottom-top); pMatrixElems[2][2] = (far+near)/(far-near); pMatrixElems[2][3] = -(2f*far*near)/(far-near); pMatrixElems[3][2] = 1f; pMatrixElems[3][3] = 0f; this.compose(pMatrix); } public void rotate(float ax, float ay, float az, float angle) { float aNormal, axHat, ayHat, azHat; float cosTheta, sinTheta; Matrix3D tempMatrix = temp1; tempMatrix.loadIdentity(); float[][] tempMatrixElems = tempMatrix.getElements(); cosTheta = (float)Math.cos(angle); sinTheta = (float)Math.sin(angle); // Normalize the axis of rotation aNormal = (float)Math.sqrt(ax*ax + ay*ay + az*az); axHat = ax/aNormal; ayHat = ay/aNormal; azHat = az/aNormal; // Combine more mults? float SymACoeffX = (1f - cosTheta)*axHat; float SymACoeffY = (1f - cosTheta)*ayHat; tempMatrixElems[0][0] = SymACoeffX*axHat + cosTheta; tempMatrixElems[0][1] = SymACoeffX*ayHat + (-azHat*sinTheta); tempMatrixElems[0][2] = SymACoeffX*azHat + ( ayHat*sinTheta); tempMatrixElems[1][0] = SymACoeffX*ayHat + ( azHat*sinTheta); tempMatrixElems[1][1] = SymACoeffY*ayHat + cosTheta; tempMatrixElems[1][2] = SymACoeffY*azHat + (-axHat*sinTheta); tempMatrixElems[2][0] = SymACoeffX*azHat + (-ayHat*sinTheta); tempMatrixElems[2][1] = SymACoeffY*azHat + ( axHat*sinTheta); tempMatrixElems[2][2] = (1f-cosTheta)*azHat*azHat + cosTheta; this.sparseCompose(tempMatrix); } public void scale(float sx, float sy, float sz) { m_elems[0][0] *= sx; m_elems[1][1] *= sy; m_elems[2][2] *= sz; translate(((1 - sx) * m_elems[0][3]), ((1 - sy) * m_elems[1][3]), ((1 - sz) * m_elems[2][3])); } public void shear(float kxy, float kxz, float kyz) { float[][] tempElems = m_elems; tempElems[0][2] += kxz*tempElems[0][0] + kyz*tempElems[0][1]; tempElems[1][2] += kxz*tempElems[1][0] + kyz*tempElems[1][1]; tempElems[2][2] += kxz*tempElems[2][0] + kyz*tempElems[2][1]; tempElems[3][2] += kxz*tempElems[3][0] + kyz*tempElems[3][1]; tempElems[0][1] += kxy*tempElems[0][0]; tempElems[1][1] += kxy*tempElems[1][0]; tempElems[2][1] += kxy*tempElems[2][0]; tempElems[3][1] += kxy*tempElems[3][0]; } public final void sparseCompose(Matrix3D src) { float[][] newElems = { {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0} }; float[][] srcElems = src.getElements(); float[][] tempElems = m_elems; for (int j = 0; j < 4; j++) { for (int i = 0; i < 3; i++) { newElems[j][i] = tempElems[j][0] * srcElems[0][i] + tempElems[j][1] * srcElems[1][i] + tempElems[j][2] * srcElems[2][i]; } newElems[j][3] = tempElems[j][3]; } m_elems = newElems; } public void transform(Point3D in[], Point3D out[], int start, int length) { int end; float in_x, in_y, in_z; float normalizer; float[][] tempElems; end = start + length; tempElems = m_elems; for (; start < end; start++) { in_x = in[start].x; in_y = in[start].y; in_z = in[start].z; //System.out.println("Transforming: " + start + ", " + in_x + ", " + // in_y + ", " + in_z); normalizer = (in_x * tempElems[3][0] + in_y * tempElems[3][1] + in_z * tempElems[3][2] + tempElems[3][3]); out[start].x = (in_x * tempElems[0][0] + in_y * tempElems[0][1] + in_z * tempElems[0][2] + tempElems[0][3]); out[start].y = (in_x * tempElems[1][0] + in_y * tempElems[1][1] + in_z * tempElems[1][2] + tempElems[1][3]); out[start].z = (in_x * tempElems[2][0] + in_y * tempElems[2][1] + in_z * tempElems[2][2] + tempElems[2][3]); if (normalizer != 1) { out[start].x /= normalizer; out[start].y /= normalizer; out[start].z /= normalizer; } out[start].argb = in[start].argb; out[start].m_intensity = in[start].m_intensity; } } public void translate(float tx, float ty, float tz) { float[] tempRow; for (int j = 0; j < 4; j++) { tempRow = m_elems[j]; tempRow[3] = tempRow[0]*tx + tempRow[1]*ty + tempRow[2]*tz + tempRow[3]; } } public String toString() { String out = ""; out += "["; for (int j = 0; j < 4; j++) { for (int i = 0; i < 4; i++) { out += " " + m_elems[j][i]; } out += "\n "; } out += "]"; return out; } // // Utility methods // public static final void add(Matrix3D m1, Matrix3D m2, int rows, int cols) { float[][] m1Elements, m2Elements; m1Elements = m1.getElements(); m2Elements = m2.getElements(); for (int j = 0; j < rows; j++) { for (int i = 0; i < cols; i++) { m1Elements[j][i] += m2Elements[j][i]; } } } public void loadIdentity() { for (int arr = 0; arr < 4; arr++) { System.arraycopy(IDENTITY_ELEMS[arr], 0, m_elems[arr], 0, 4); } } public final void mulByScalar(float scalar, int rows, int cols) { for (int j = 0; j < rows; j++) { for (int i = 0; i < cols; i++) { m_elems[j][i] *= scalar; } } } public static Matrix3D makeNormalMatrix(Matrix3D m) { float[][] m_elems; m_elems = m.getElements(); // // The closed-form soln. for the normal matrix, in terms // of matrix m float[][] newElems = { { // // Element 0, 0 ((m_elems[1][1]*m_elems[2][2]) - (m_elems[1][2]*m_elems[2][1])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), // // Element 1, 0 -((m_elems[1][0]*m_elems[2][2]) - (m_elems[1][2]*m_elems[2][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), // // Element 2, 0 ((m_elems[1][0]*m_elems[2][1]) - (m_elems[1][1]*m_elems[2][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), 0 }, { -((m_elems[0][1]*m_elems[2][2]) - (m_elems[0][2]*m_elems[2][1])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), ((m_elems[0][0]*m_elems[2][2]) - (m_elems[0][2]*m_elems[2][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), -((m_elems[0][0]*m_elems[2][1]) - (m_elems[0][1]*m_elems[2][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), 0 }, { ((m_elems[0][1]*m_elems[1][2]) - (m_elems[0][2]*m_elems[1][1])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), -((m_elems[0][0]*m_elems[1][2]) - (m_elems[0][2]*m_elems[1][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), ((m_elems[0][0]*m_elems[1][1]) - (m_elems[0][1]*m_elems[1][0])) / ((m_elems[0][0]*m_elems[1][1]*m_elems[2][2]) - (m_elems[0][0]*m_elems[1][2]*m_elems[2][1]) - (m_elems[1][0]*m_elems[0][1]*m_elems[2][2]) + (m_elems[1][0]*m_elems[0][2]*m_elems[2][1]) + (m_elems[2][0]*m_elems[0][1]*m_elems[1][2]) - (m_elems[2][0]*m_elems[0][2]*m_elems[1][1])), 0 }, { 0, 0, 0, 1} }; Matrix3D ret = new Matrix3D(); float[][] retElems = ret.getElements(); for (int arr = 0; arr < 4; arr++) { System.arraycopy(newElems, 0, retElems, 0, 4); } return ret; } public static Matrix3D makeNormalMatrix2(Matrix3D m) { Matrix3D ret = new Matrix3D(); float[][] mElems = m.getElements(); float[][] retElems = ret.getElements(); float[][] newElems = { { mElems[0][0], mElems[0][1], mElems[0][2], 0 }, { mElems[1][0], mElems[1][1], mElems[1][2], 0 }, { mElems[2][0], mElems[2][1], mElems[2][2], 0 }, { 0, 0, 0, 1 } }; for (int arr = 0; arr < 4; arr++) { System.arraycopy(retElems, 0, newElems, 0, 4); } ret.inverse(); ret.transpose(); return ret; } public void transpose() { float tmp; for (int j = 0; j < 4; j++) { for (int i = j; i < 4; i++) { tmp = m_elems[i][j]; m_elems[i][j] = m_elems[j][i]; m_elems[j][i] = tmp; } } } public void inverse() { Matrix3D ident = new Matrix3D(); float[][] i_elems = ident.getElements(); for (int j = 0; j < 4; j++) { for (int i = 0; i < j; i++) { if (m_elems[j][i] != 0) { float factorM = m_elems[j][i] / m_elems[i][i]; for (int k = 0; k < 4; k++) { i_elems[j][k] -= i_elems[i][k] * factorM; m_elems[j][k] -= m_elems[i][k] * factorM; } } } } for (int j = 0; j < 4; j++) { for (int i = j + 1; i < 4; i++) { if (m_elems[j][i] != 0) { float factorM = m_elems[j][i] / m_elems[i][i]; for (int k = 0; k < 4; k++) { i_elems[j][k] -= i_elems[i][k] * factorM; m_elems[j][k] -= m_elems[i][k] * factorM; } } } } for (int i = 0; i < 4; i++) { float factor = 1 / m_elems[i][i]; for (int k = 0; k < 4; k++) { i_elems[i][k] *= factor; m_elems[i][k] *= factor; } } m_elems = i_elems; } static { temp1 = new Matrix3D(); } }